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Matrix mechanics was the first complete and correct definition of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps occur. It did so by interpreting the physical properties of particles as matrices which evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra-ket notation for the wave function.
After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point: On July 9 Heisenberg gave the same paper of his calculations to Max Born, saying: prior to publication. Heisenberg then departed for a while, leaving Born to analyse the paper.
In the paper, Heisenberg formulated quantum theory without sharp electron orbits. Hendrik Kramers had earlier calculated the relative intensities of spectral lines in the Sommerfeld model by interpreting the Fourier coefficients of the orbits as intensities. But his answer, like all other calculations in the old quantum theory, was only correct for large orbits.
Heisenberg, after a collaboration with Kramers, began to understand that the transition probabilities were not quite classical quantities, because the only frequencies that appear in the Fourier series should be the ones that are observed in quantum jumps, not the fictional ones that come from Fourier-analyzing sharp classical orbits. He replaced the classical Fourier series with a matrix of coefficients, a fuzzed-out quantum analog of the Fourier series. Classically, the Fourier coefficients give the intensity of the emitted radiation, so in quantum mechanics the magnitude of the matrix elements were the intensities of spectral lines.
The quantities in Heisenberg's formulation were the classical position and momentum, but now they were no longer sharply defined. Each quantity was represented by a collection of Fourier coefficients with two indices, corresponding to the initial and final states. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors. (A brief review of Born's role in the development of the matrix mechanics formulation of quantum mechanics along with a discussion of the key formula involving the non-commutivity of the probability amplitudes can be found in an article by Jeremy Bernstein. A detailed historical and technical account can be found in Mehra and Rechenberg's book The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925–1926.)
Up until this time, matrices were seldom used by physicists, they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. Born, however, had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert's theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert's work Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen published in 1912. Jordan, too was well equipped for the task. For a number of years, he had been an assistant to Richard Courant at Göttingen in the preparation of Courant and David Hilbert's book Methoden der mathematischen Physik I, which was published in 1924. This book, fortuitously, contained a great many of the mathematical tools necessary for the continued development of quantum mechanics. In 1926, John von Neumann became assistant to David Hilbert, and he would coin the term Hilbert space to describe the algebra and analysis which were used in the development of quantum mechanics.
Before matrix mechanics, the old quantum theory described the motion of a particle by a classical orbit with the restriction that the time integral over one period T of the momentum times the velocity must be a positive integer multiple of Planck's constant
While this restriction correctly selects orbits with more or less the right energy values , the old quantum mechanical formalism did not describe time dependent processes, such as the emission or absorption of radiation.
When a classical particle is weakly coupled to a radiation field, so that the radiative damping can be neglected, it will emit radiation in a pattern which repeats itself every orbital period. The frequencies which make up the outgoing wave are then integer multiples of the orbital frequency, and this is a reflection of the fact that X(t) is periodic, so that its Fourier representation has frequencies only.
The coefficients are complex numbers. The ones with negative frequencies must be the complex conjugates of the ones with positive frequencies, so that X(t) will always be real,
A quantum mechanical particle, on the other hand, can't emit radiation continuously, it can only emit photons. Assuming that the quantum particle started in orbit number n, emitted a photon, then ended up in orbit number m, the energy of the photon is , which means that its frequency is .
For large n and m, but with n-m relatively small, these are the classical frequencies by Bohr's correspondence principle
In the formula above, T is the classical period of either orbit n or orbit m, since the difference between them is higher order in h. But for n and m small, or if is large, the frequencies are not integer multiples of any single frequency.
Since the frequencies which the particle emits are the same as the frequencies in the fourier description of its motion, this suggests that something in the time-dependent description of the particle is oscillating with frequency . Heisenberg called this quantity , and demanded that it should reduce to the classical Fourier coefficients in the classical limit. For large values of n, m but with n-m relatively small, is the (n-m)th fourier coefficient of the classical motion at orbit n. Since has opposite frequency to , the condition that X is real becomes:
By definition, only has the frequency , so its time evolution is simple:
This is the original form of Heisenberg's equation of motion.
Given two arrays and describing two physical quantities, Heisenberg could form a new array of the same type by combining the terms , which also oscillate with the right frequency. Since the Fourier coefficients of the product of two quantities is the convolution of the Fourier coefficients of each one separately, the correspondence with Fourier series allowed Heisenberg to deduce the rule by which the arrays should be multiplied:
Born pointed out that this is the law of matrix multiplication, so that the position, the momentum, the energy, all the observable quantities in the theory, are interpreted as matrices. Because of the multiplication rule, the product depends on the order: XP is different from PX.
The X matrix is a complete description of the motion of a quantum mechanical particle. Because the frequencies in the quantum motion are not multiples of a common frequency, the matrix elements cannot be interpreted as the Fourier coefficients of a sharp classical trajectory. Nevertheless, as matrices, and satisfy the classical equations of motion.
When it was introduced by Werner Heisenberg, Max Born and Pascual Jordan in 1925, matrix mechanics was not immediately accepted and was a source of great controversy. Schrödinger's later introduction of wave mechanics was favored.
Part of the reason was that Heisenberg's formulation was in a strange new mathematical language, while Schrödinger's formulation was based on familiar wave equations. But there was also a deeper sociological reason. Quantum mechanics had been developing by two paths, one under the direction of Einstein and the other under the direction of Bohr. Einstein emphasized wave-particle duality, while Bohr emphasized the discrete energy states and quantum jumps. DeBroglie had shown how to reproduce the discrete energy states in Einstein's framework--- the quantum condition is the standing wave condition, and this gave hope to those in the Einstein school that all the discrete aspects of quantum mechanics would be subsumed into a continuous wave mechanics.
Matrix mechanics, on the other hand, came from the Bohr school, which was concerned with discrete energy states and quantum jumps. Bohr's followers did not appreciate physical models which pictured electrons as waves, or as anything at all. They preferred to focus on the quantities which were directly connected to experiments.
In atomic physics, spectroscopy gave observational data on atomic transitions arising from the interactions of atoms with light quanta. The Bohr school required that only those quantities which were in principle measurable by spectroscopy should appear in the theory. These quantities include the energy levels and their intensities but they do not include the exact location of a particle in its Bohr orbit. It is very hard to imagine an experiment which could determine whether an electron in the ground state of a hydrogen atom is to the right or to the left of the nucleus. It was a deep conviction that such questions did not have an answer.
The matrix formulation was built on the premise that all physical observables are represented by matrices whose elements are indexed by two different energy levels. The set of eigenvalues of the matrix were eventually understood to be the set of all possible values that the observable can have. Since Heisenberg's matrices are Hermitian, the eigenvalues are real.
If an observable is measured and the result is a certain eigenvalue, the corresponding eigenvector is the state of the system immediately after the measurement. The act of measurement in matrix mechanics 'collapses' the state of the system. If you measure two observables simultaneously, the state of the system should collapse to a common eigenvector of the two observables. Since most matrices don't have any eigenvectors in common, most observables can never be measured precisely at the same time. This is the uncertainty principle.
If two matrices share their eigenvectors, they can be simultaneously diagonalized. In the basis where they are both diagonal, it is clear that their product does not depend on their order because multiplication of diagonal matrices is just multiplication of numbers. The Uncertainty Principle then is a consequence of the fact that two matrices A and B do not always commute, A B - B A does not necessarily equal 0. The famous commutation relation of matrix mechanics:
shows that there are no states which simultaneously have a definite position and momentum. But the principle of uncertainty (also called complementarity by Bohr) holds for most other pairs of observables too. For example, the energy does not commute with the position either, so it is impossible to precisely determine the position and energy of an electron in an atom.
In 1925, Werner Heisenberg was not yet 24 years old.
In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, but it was not to be. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen" and Erwin Schrödinger and Paul Adrien Maurice Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory". One can rightly ask why Born was not awarded the Prize in 1932 along with Heisenberg, and Bernstein gives some speculations on this matter. One of them is related to Jordan joining the Nazi Party on May 1, 1933 and becoming a Storm Trooper. Hence, Jordan's Party affiliations and Jordan's links to Born may have affected Born's chance at the Prize at that time. Bernstein also notes that when Born won the Prize in 1954, Jordan was still alive, and the Prize was awarded for the statistical interpretation of quantum mechanics, attributable alone to Born.
Heisenberg's reaction to Born for Heisenberg receiving the Prize for 1932 and to Born for Born receiving the Prize in 1954 are also instructive in evaluating whether Born should have shared the Prize with Heisenberg. On November 25, 1933 Born received a letter from Heisenberg in which he said he had been delayed in writing due to a "bad conscience" that he alone had received the Prize "for work done in Göttingen in collaboration – you, Jordan and I." Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside." In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not "adequately acknowledged in the public eye."
Once Heisenberg introduced the matrices for X and P, he could find their matrix elements in special cases by guesswork, guided by the correspondence principle. Since the matrix elements are the quantum mechanical analogs of Fourier coefficients of the classical orbits, the simplest case is the harmonic oscillator, where X(t) and P(t) are sinusoidal.
In units where the mass and frequency of the oscillator are equal to one, the energy of the oscillator is
The level sets of H are the orbits, and they are nested circles. The classical orbit with energy E is:
The old quantum condition says that the integral of P dX over an orbit, which is the area of the circle in phase space, must be an integer multiple of Planck's constant. The area of the circle of radius is So
or, in units of length where is one, the energy is an integer.
The Fourier components of X(t) and P(t) are very simple, even more so if they are combined into the quantities:
both and have only a single frequency, and and can be recovered from their sum and difference.
Since has a classical fourier series with only the lowest frequency, and the matrix element is the (m-n)th fourier coefficient of the classical orbit, the matrix for is nonzero only on the line just above the diagonal, where it is equal to . The matrix for is likewise only nonzero on the line below the diagonal, with the same elements. Reconstructing X and P from and :
which, up to the choice of units, are the Heisenberg matrices for the harmonic oscillator. Notice that both matrices are hermitian, since they are constructed from the Fourier coefficients of real quantities. To find and is simple, since they are quantum Fourier coefficients so they evolve simply with time.
The matrix product of and is not hermitian, but has a real and imaginary part. The real part is one half the symmetric expression , while the imaginary part is proportional to the commutator . It is easy to verify explicitly that in the case of the harmonic oscillator, is i, multiplied by the identity. It is also easy to verify that the matrix
The harmonic oscillator is too special. It is too easy to find the matrices exactly, and it is too hard to discover general conditions from these special forms. For this reason, Heisenberg investigated the anharmonic oscillator, with Hamiltonian
In this case, the X and P matrices are no longer simple off diagonal matrices, since the corresponding classical orbits are slightly squashed and displaced, so that they have Fourier coefficients at every classical frequency. To determine the matrix elements, Heisenberg required that the classical equations of motion be obeyed as matrix equations:
He noticed that if this could be done then H considered as a matrix function of X and P, will have zero time derivative.
Given that all the off diagonal elements have a nonzero frequency; H being constant implies that H is diagonal. It was clear to Heisenberg that in this system, the energy could be exactly conserved in an arbitrary quantum system, a very encouraging sign.
The process of emission and absorption of photons seemed to demand that the conservation of energy will hold at best on average. If a wave containing exactly one photon passes over some atoms, and one of them absorbs it, that atom needs to tell the others that they can't absorb the photon anymore. But if the atoms are far apart, any signal cannot reach the other atoms in time, and they might end up absorbing the same photon anyway and dissipating the energy to the environment. When the signal reached them, the other atoms would have to somehow recall that energy. This paradox led Bohr, Kramers and Slater to abandon exact conservation of energy. Heisenberg's formalism, when extended to include the electromagnetic field, was obviously going to sidestep this problem, a hint that the interpretation of the theory will involve wavefunction collapse.
Demanding that the classical equations of motion are preserved is not a strong enough condition to determine the matrix elements. Planck's constant does not appear in the classical equations, so that the matrices could be constructed for many different values of and still satisfy the equations of motion, but with different energy levels.
So in order to implement his program, Heisenberg needed to use the old quantum condition to fix the energy levels, then fill in the matrices with Fourier coefficients of the classical equations, then alter the matrix coefficients and the energy levels slightly to make sure the classical equations are satisfied. This is clearly not satisfactory. The old quantum conditions refer to the area enclosed by the sharp classical orbits, which do not exist in the new formalism.
The most important thing that Heisenberg discovered is how to translate the old quantum condition into a simple statement in matrix mechanics. To do this, he investigated the action integral as a matrix quantity:
There are several problems with this integral, all stemming from the incompatibility of the matrix formalism with the old picture of orbits. Which period T should you use? Semiclassically, it should be either m or n, but the difference is order h and we want an answer to order h. The quantum condition tells us that is on the diagonal, then the fact that J is classically constant tells us that the off diagonal elements are zero.
His crucial insight was to differentiate the quantum condition with respect to n. This idea only makes complete sense in the classical limit, where n is not an integer but the continuous action variable J, but Heisenberg performed analogous manipulations with matrices, where the intermediate expressions are sometimes discrete differences and sometimes derivatives. In the following discussion, for the sake of clarity, the differentiation will be performed on the classical variables, and the transition to matrix mechanics will be done afterwards using the correspondence principle.
In the classical setting, the derivative is the derivative with respect to J of the integral which defines J, so it is tautologically equal to 1.
Where the derivatives dp/dJ dx/dJ should be interpreted as differences with respect to J at corresponding times on nearby orbits, exactly what you would get if you differentiated the Fourier coefficients of the orbital motion. These derivatives are symplectically orthogonal in phase space to the time derivatives dP/dt dX/dt. The final expression is clarified by introducing the variable canonically conjugate to J, which is called the angle variable . The derivative with respect to time is a derivative with respect to , up to a factor of .
So the quantum condition integral is the average value over one cycle of the Poisson bracket of X and P. An analogous differentiation of the Fourier series of P dX demonstrates that the off diagonal elements of the Poisson bracket are all zero. The Poisson bracket of two canonically conjugate variables, such as X and P, is the constant value 1, so this integral really is the average value of 1, so it is 1, as we knew all along, because it is dJ/dJ after all. But Heisenberg, Born and Jordan weren't familiar with the theory of Poisson brackets, so for them, the differentiation effectively evaluated {X,P} in J coordinates.
The Poisson Bracket, unlike the action integral, has a simple translation to matrix mechanics--- it is the imaginary part of the product of two variables, the commutator. To see this, examine the product of two matrices A and B in the correspondence limit, where the matrix elements are slowly varying functions of the index, keeping in mind that the answer is zero classically.
In the correspondence limit, when indices m n are large and nearby, while k,r are small, the rate of change of the matrix elements in the diagonal direction is the matrix element of the J derivative of the corresponding classical quantity. So we can shift any matrix element diagonally using the formula:
Where the right hand side is really only the (m-n)'th Fourier component of (dA/dJ) at orbit near m to this semiclassical order, not a full well defined matrix.
The semiclassical time derivative of a matrix element is obtained up to a factor of i by multiplying by the distance from the diagonal,
Since the coefficient is semiclassically the k'th Fourier coefficient of the m-th classical orbit.
The imaginary part of the product of A and B can be evaluated by shifting the matrix elements around so as to reproduce the classical answer, which is zero. The leading nonzero residual is then given entirely by the shifting. Since all the matrix elements are at indices which have a small distance from the large index position , it helps to introduce two temporary notations: , for the matrices, and for the r'th Fourier components of classical quantities.
Flipping the summation variable in the first sum from r to r'=k-r, the matrix element becomes:
and it is clear that the main part cancels. The leading quantum part, neglecting the higher order product of derivatives, is
which can be identified as i times the k-th classical Fourier component of the Poisson bracket. Heisenberg's original differentiation trick of was eventually extended to a full semiclassical derivation of the quantum condition in collaboration with Born and Jordan.
Once they were able to establish that:
this condition replaced and extended the old quantization rule, allowing the matrix elements of P and X for an arbitrary system to be determined simply from the form of the Hamiltonian. The new quantization rule was assumed to be universally true, even though the derivation from the old quantum theory required semiclassical reasoning.
To make the transition to modern quantum mechanics, the most important further addition was the quantum state vector, now written , which is the vector that the matrices act on. Without the state vector, it is not clear which particular motion the Heisenberg matrices are describing, since they include all the motions somewhere.
The interpretation of the state vector, whose components are written , was given by Born. The interpretation is statistical: the result of a measurement of the physical quantity corresponding to the matrix A is random, with an average value equal to
Alternatively and equivalently, the state vector gives the probability amplitude for the quantum system to be in the energy state i. Once the state vector was introduced, matrix mechanics could be rotated to any basis, where the H matrix was no longer diagonal. The Heisenberg equation of motion in its original form states that evolves in time like a Fourier component
which can be recast in differential form
and it can be restated so that it is true in an arbitrary basis by noting that the H matrix is diagonal with diagonal values :
This is now a matrix equation, so it holds in any basis. This is the modern form of the Heisenberg equation of motion. The formal solution is:
All the forms of the equation of motion above say the same thing, that A(t) is equal to A(0) up to a basis rotation by the unitary matrix . By rotating the basis for the state vector at each time by , you can undo the time dependence in the matrices. The matrices are now time independent, but the state vector rotates:
This is the Schroedinger equation for the state vector, and the time dependent change of basis is the transformation to the Schroedinger picture.
In quantum mechanics in the Heisenberg picture the state vector, does not change with time, and an observable A satisfies
The extra term is for operators like which have an explicit time dependence in addition to the time dependence from unitary evolution. The Heisenberg picture does not distinguish time from space, so it is nicer for relativistic theories.
Moreover, the similarity to classical physics is more obvious: the Hamiltonian equations of motion for classical mechanics are recovered by replacing the commutator above by the Poisson bracket.
By the Stone-von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent.
See also Schrödinger picture.
Matrix mechanics rapidly developed into modern quantum mechanics, and gave interesting physical results on the spectra of atoms.
Jordan noted that the commutation relations ensure that p acts as a differential operator, and came very close to formulating the Schrödinger equation. The identity
allows the evaluation of the commutator of p with any power of x, and it implies that
which, together with linearity, implies that a p commutator differentiates any analytic matrix function of x. Assuming limits are defined sensibly, this will extend to arbitrary functions, but the extension does not need to be made explicit until a certain degree of mathematical rigor is required.
Since x is a Hermitian matrix, it should be diagonalizable, and it will be clear from the eventual form of p that every real number can be an eigenvalue. This makes some of the mathematics subtle, since there is a separate eigenvector for every point in space. In the basis where x is diagonal, an arbitrary state can be written as a superposition of states with eigenvalues x:
and the operator x multiplies each eigenvector by x.
Define a linear operator D which differentiates :
so that the operator - iD obeys the same commutation relation as p. The difference between p and - iD must commute with x.
rotating each state |x> by a phase f(x), that is, redefining the phase of the wavefunction:
the operator iD is redefined by an amount:
which means that in the rotated basis, p is equal to -iD. So there is always a basis for the eigenvalues of x where the action of p on any wavefunction is known:
and the Hamiltonian in this basis is a linear differential operator on the state vector components:
So that the equation of motion for the state vector is the differential equation:
Since D is a differential operator, in order for it to be sensibly defined, there must be eigenvalues of x which neighbor every given value. This suggests that the only possibility is that the space of all eigenvalues of x is all real numbers, and that p is iD up to the phase rotation. To make this rigorous requires a sensible discussion of the limiting space of functions, and in this space this is the Stone-von Neumann theorem--- any operators x and p which obey the commutation relations can be made to act on a space of wavefunctions, with p a derivative operator. This implies that a Schrödinger picture is always available.
Unlike the Schrödinger approach, matrix mechanics could be extended to many degrees of freedom in an obvious way. Each degree of freedom has a separate x operator and a separate differential operator p, and the wavefunction is a function of all the possible eigenvalues of the independent commuting x variables.
In particular, this means that a system of N interacting particles in 3 dimensions are described by one vector whose components in a basis where all the X are diagonal is a mathematical function of 3N dimensional space which describes all their possible positions, which is a much bigger collection of values than N three dimensional wavefunctions in physical space. Schrödinger came to the same conclusion independently, and eventually proved the equivalence of the his own formalism to Heisenberg's.
Since the wavefunction is a property of the whole system, not of any one part, the description in quantum mechanics is not entirely local. The description of several particles can be quantumly correlated, or entangled. This entanglement leads to strange correlations between distant particles which violate the classical Bell's inequality.
Even if the particles can only be in two positions, the wavefunction for N particles requires complex numbers, one for each configuration of positions. This is exponentially many numbers in N, so simulating quantum mechanics on a computer requires exponential resources. This suggests that it might be possible to find quantum systems of size N which physically compute the answers to problems which classically require bits to solve, which is the motivation for quantum computing.
In classical mechanics, a canonical transformation of phase space coordinates is one which preserves the structure of the Poisson brackets. The new variables x',p' have the same Poisson brackets with each other as the original variables x,p. Time evolution is a canonical transformation, since the phase space at any time is just as good a choice of variables as the phase space at any other time.
The Hamiltonian flow is then the canonical canonical transformation:
Since the Hamiltonian can be an arbitrary function of x and p, there are infinitesimal canonical transformations corresponding to every classical quantity G, where G is used as the Hamiltonian to generate a flow of points in phase space for an increment of time s.
For a general function A(x,p) on phase space, the infinitesimal change at every step ds under the map is:
The quantity G is called the infinitesimal generator of the canonical transformation.
In quantum mechanics, G is a Hermitian matrix, and the equations of motion are commutators:
The infinitesimal canonial motions can be formally integrated, just as the Heisenberg equation of motion were integrated:
where and s is an arbitrary parameter. The definition of a canonical transformation is an arbitrary unitary change of basis on the space of all state vectors. U is an arbitrary unitary matrix, a complex rotation in phase space.
The interpretation of the matrices is that they act as generators of motions on the space of states. The motion generated by P can be found by solving the Heisenberg equation of motion using P as the Hamiltonian:
They are translations of the matrix X which add a multiple of the identity: . This is also the interpretation of the derivative operator D , the exponential of a derivative operator is a translation. The X operator likewise generates translations in P. The Hamiltonian generates translations in time, the angular momentum generates rotations in physical space, and the operator generates rotations in phase space.
When a transformation, like a rotation in physical space, commutes with the Hamiltonian, the transformation is called a symmetry. The Hamiltonian expressed in terms of rotated coordinates is the same as the original Hamiltonian. This means that the change in the Hamiltonian under the infinitesimal generator L is zero:
It follows that the change in the generator under time translation is also zero:
So that the matrix L is constant in time. The one-to-one association of infinitesimal symmetry generators and conservation laws was first discovered by Emmy Noether for classical mechanics, where the commutators are Poisson brackets but the argument is identical.
In quantum mechanics, any unitary symmetry transformation gives a conservation law, since if the matrix U has the property that
The eigenvalues of unitary matrices are pure phases, so that the value of a unitary conserved quantity is a complex number of unit magnitude, not a real number. Another way of saying this is that a unitary matrix is the exponential of i times a Hermitian matrix, so that the additive conserved real quantity, the phase, is only well defined only up to an integer multiple of 2pi. Only when the unitary symmetry matrix is part of a family that comes arbitrarily close to the identity are the conserved real quantities single-valued, and then the demand that they are conserved become a much more exacting constraint.
Symmetries which can be continuously connected to the identity are called continuous, and translations, rotations, and boosts are examples. Symmetries which cannot be continuously connected to the identity are discrete, and the operation of space-inversion, or parity, and charge conjugation are examples.
The interpretation of the matrices as generators of canonical trasformations is due to Paul Dirac. The correspondence between symmetries and matrices was shown by Eugene Wigner to be complete, if antiunitary matrices which describe symmetries which include time-reversal are included.
It was physically clear to Heisenberg that the absolute squares of the matrix elements of X, which are the fourier coefficients of the oscillation, would be the rate of emission of electromagnetic radiation.
In the classical limit of large orbits, if a charge with position X(t) and charge q is oscillating next to an equal and opposite charge at position 0, the instantaneous dipole moment is qX(t), and the time variation of the moment translates directly into the space-time variation of the vector potential, which produces nested outgoing spherical waves. For atoms the wavelength of the emitted light is about 10,000 times the atomic radius, the dipole moment is the only contribution to the radiative field and all other details of the atomic charge distribution can be ignored.
Ignoring back-reaction, the power radiated in each outgoing mode is a sum of separate contributions from the square of each independent time Fourier mode of d:
And in Heisenberg's representation, the Fourier coefficients of the dipole moment are the matrix elements of X. The correspondence allowed Heisenberg to provide the rule for the transition intensities, the fraction of the time that, starting from an initial state i, a photon is emitted and the atom jumps to a final state j:
This allowed the magnitude of the matrix elements to be interpreted statistically--- they give the intensity of the spectral lines, the probability for quantum jumps from the emission of dipole radiation.
Since the transition rates are given by the matrix elements of X, wherever is zero, the corresponding transition should be absent. These were called the selection rules, and they were a puzzle before matrix mechanics.
An arbitrary state of the Hydrogen atom, ignoring spin, is labelled by |n;l,m>, where the value of l is a measure of the total orbital angular momentum and m is its z-component, which defines the orbit orientation.
The components of the angular momentum pseudovector are:
The commutation relations of L with x (or with any vector) are easy to find:
From this, the commutator of L_z and the coordinate matrices x,y,z can be read off,
Which means that the quantities x+iy,x-iy have a simple commutation rule:
Just like the matrix elements of x+ip and x-ip for the harmonic oscillator hamiltonian, this commutation law implies that these operators only have certain off diagonal matrix elements in states of definite m.
meaning that the matrix (x+iy) takes an eigenvector of with eigenvalue m to an eigenvector with eigenvalue m+1. Similarly, (x-iy) decrease m by one unit, and z does not change the value of m.
So in a basis of |l,m> states where and have definite values, the matrix elements of any of the three components of the position are zero except when m is the same or changes by one unit.
This places a constraint on the change in total angular momentum. Any state can be rotated so that its angular momentum is in the z-direction as much as possible, where m=l. The matrix element of the position acting on |l,m> can only produce values of m which are bigger by one unit, so that if the coordinates are rotated so that the final state is |l',l'>, the value of l' can be at most one bigger than the biggest value of l that occurs in the initial state. So l' is at most l+1. The matrix elements vanish for l'>l+1, and the reverse matrix element is determined by Hermiticity, so these vanish also when l' The Heisenberg equation of motion determine the matrix elements of p in the Heisenberg basis from the matrix elements of x. which turns the diagonal part of the commutation relation into a sum rule for the magnitude of the matrix elements: This gives a relation for the sum of the spectroscopic intensities to and from any given state, although to be absolutely correct, contributions from the radiative capture probability for unbound scattering states must be included in the sum:
p_{ij} = m{dover dt} x_{ij} = im (E_i - E_j) x_{ij}
sum_j p_{ij}x_{ji} - x_{ij}p_{ji} = i sum_j 2m(E_i - E_j) |x_{ij}|^2 = i.
sum_j 2m(E_i - E_j) |x_{ij}|^2 = 1.
The three formulating papers
See also
External links
The Heisenberg equation of motion determine the matrix elements of p in the Heisenberg basis from the matrix elements of x.
which turns the diagonal part of the commutation relation into a sum rule for the magnitude of the matrix elements:
This gives a relation for the sum of the spectroscopic intensities to and from any given state, although to be absolutely correct, contributions from the radiative capture probability for unbound scattering states must be included in the sum:


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All Politics are Local
Kentuckian Frontrunner for U.S. Ambassadorship to Britain
By Joseph Lord & Kentucky Public Radio
Kentuckian Matthew Barzun will be the U.S. to the United Kingdom if he wants the job, The New York Times has reported, citing donors and adviser to President Obama. Barzun, a former tech executive and major Obama fundraiser, has been the front-runner for the prestigious post since November, The Times reported. If the reports are true, he'd beat out for the job the famed editor of Vogue magazine, Anna Wintour.

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Woodland Police Officers, 1935
The Woodland Police Department was created with the election of a City Marshall in 1871, just after the City of Woodland was incorporated.
The first Marshall elected was John D. Lawson, who received a salary of $1000 per year. In 1874 a night watchman was elected to assist the Marshall. This position, later know as a policeman, was primarily for "traffic enforcement" of horses, mules and wagons in downtown.
Officer Larry L. Sills
On June 7, 1945 while pursuing a suspect vehicle, he hit a patch of loose gravel and lost control of his motorcycle. Hospitalized as a result of the injuries he sustained, he passed away on June 13. Officer Sills was survived by his wife, Lucinda Messick, and two daughters: Nancy Rogers and Sue Goodall.


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by Grand Forks Herald
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MAC 224 Tapered Blending Brush Photos & Review
Beauty Basics: MAC Eye Brushes
Beauty Basics is a series covering basic products and tools that help to make applying your makeup easier. To view the entire series to date, be sure to visit the beauty basics, or you can view posts within the series about MAC Eye Brushes.
Focus On: MAC 224 Tapered Blending Brush
MAC 224 Tapered Blending Brush ($28.00) is a long, fluffy brush with a dome-shaped tip designed for assisting you with blending out color. It can also be used to deposit color more subtly for those who need softer application. I do like using this as a highlighter, both on the face or on the brow bone. It's not a brush I reach for often, as I tend to favor other brushes, but for some, this brush outdoes brushes like the 217 and 222. The fluffiness of this brush also makes it good for applying creamier products, like concealer, in hard to reach places (e.g. around the nose). The 224 is one of those brushes that many people swear by, and others will say they prefer another brush (e.g. the 222), so it's most definitely worth taking a peek at next time you're at a MAC store. It will certainly help you out with blending if that's ever been a problem for you!
How to decide between the 222 and 224? Think about what you're going to use it for. If you're looking for a brush primarily to help blend or deposit crease colors, you might opt for the 222 since it is narrower and thus allows for more control. If you're more concerned with blending crease colors, the 224 makes it a cinch!
How do you like to use this brush?
See close-ups…
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Chuck is a young adult Basenji/Beagle mix. He is kennel trained full grown and great with other dogs. This adorable dog is fantastic For more information about Chuck or any of the other animals ready for adoption contact the Washington County/Johnson City Animal Shelter at 926-8769 from 12-5 seven days a week.
Ron Campbell/Johnson City Press


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Katy Perry Unfollows Russell Brand on Twitter — But Is He Still Following Her?
If we heard that one of our exes was possibly planning to write a scathing tell-all book about our relationship, we'd probably unfollow him on Twitter, too!
Us Weekly reports that singer Katy Perry has officially stopped following her her soon-to-be ex-husband Russell Brand on Twitter. It's been close to a month since Russell filed for divorce, and sources tell the magazine that Katy wants him out of her life.
"He's being so atrocious that she feels like she never really knew him," the source says. Yikes. Sounds intense!
For his part, Russell hasn't stopped following Katy on Twitter yet. So maybe things between the couple's state isn't as dire as we've been led to believe? Hopefully, that nasty tell-all really is just a rumor. Is a drama-free breakup really too much to ask for?
Source: Us Weekly
And if you want to get all sentimental about the Katy and Russell that was, take a look at our photo gallery of their better moments, and then have a listen to Katy's acoustic version of "The One That Got Away." We dare you to have a dry eye after listening to that!
For the latest from Wetpaint Entertainment, Like us on Facebook or Follow us on Twitter.


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Boston Marathon bombing puts increased security emphasis on Pittsburgh
Officials taking precautions for Pittsburgh Marathon on May 5UPDATED 9:00 PM EDT Apr 15, 2013
With less than three weeks to go until the Pittsburgh Marathon, Monday's bomb blasts at the Boston Marathon have placed an increased emphasis on security for the event.
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Pain in your back or neck pain is common and many different conditions and injuries can cause it. Most pain is temporary, but it can reoccur. It's often caused by a strained muscle or sprained ligament - perhaps from an activity you're not used to such as yard work, moving furniture, or sitting for a long time. Less often, pain comes from damage to part of your spine or from a condition you were born with.
It is critical that you learn the best ways to manage your back pain. There are many things that you can do to self-manage your pain and improve your quality of life. Although some individuals may need injections or even surgery, many patients will find relief and improvement through careful and consistent implementation of a self-care program.
Back pain can also come with other symptoms such as numbness, weakness, and stiffness. Symptoms may not be limited to your back or neck - you might feel them in your limbs or other areas of your body.
Anyone can have back or neck pain. Still, some things increase your chance of having pain:


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Hybrid Tiers
We have seen a shift in the automotive world to hybrid vehicles with part electric and part gas-powered motors. There are points of efficiency to operate with batteries, and then again when horsepower is needed. The intelligence of the engine control determines when the car should operate on battery or pistons, thus removing the decision-making for the driver.
Some believe hybrids are a stepping-stone technology to the day when we can have all-electric cars. The time for the hybrid (if it is a transition technology) will allow for the electric re-charging infrastructure to be built out, for the price of electric cars to come down, for the battery to become lighter and cheaper, and for the technology to allow more miles between charges. If you have been in a Toyota Prius, you may be mesmerized by the graphics on the console that shows the battery, engine and drive train schematics.
The analogy of hybrid cars may clarify where we are as a storage industry with piston disks (mechanical SATA or SAS) and the new electric motors (solid state drives). We know that all SSD systems are powerful, consume less electricity and cooling, but are expensive and have a limiting factor with the amount of volumes available in the industry today.
Are in a hybrid storage infrastructure right now?
Recently, HDS announced Hitachi Dynamic Tiering (HDT) software, which performs the intelligence of moving data and can be analogous to the engine management function of a hybrid car. The storage engineer, DBA, or application does not want to decide when to run on SATA or SAS, and when to run on SSD. These HDT pools can include SSD, SAS and SATA disks in the same LUN, and the intelligence can move high I/O pages to SSD when needed, and keep the lower-access data in SATA when appropriate.
This diagram shows how 50% of the I/O can be reserved for Tier 0 SAS, and 80% of capacity of SATA used for 20% of the I/O. Tier 1 in this example is SAS, with 15% of capacity and 30% of the I/O.
The economics or cost of tiers is dramatic with this new hybrid storage tier approach. Let's look at an example of a traditional 36TB disk configuration, with pricing, and other factors.
Page 1 of 4 | Next page


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some of us –
we never were given the chance to grow up with her.
We see a stranger when we look in the mirror
We see a girl who covers her sad eyes with pretty colors to disguise-
then blushes some pink on the very skin that held many tears along her cheeks to look alive
but none from us…
we were never aloud to cry.
Not even worth a goodbye
And off she goes… fighting for her tomorrow;
It doesn't take her long to hide the sorrow.
While we remain in today
stuck within this shell we borrow.


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Stylianou, Menelaos (1989) A computer method for dynamic analysis of HVAC system : building interaction and control applications. Masters thesis, Concordia University.
Concordia University Libraries
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Greetings from Kirkenes, Norway!
Our journey started at Raleigh-Durham International Airport, where we had to check our "carry-on" bags. Our flight was delayed so we arrived in Newark with only 20 minutes to make it to the next leg. Of course, we had to wait for the "carry-on" bags that had been checked but amazingly we made the flight to Norway (we were the last to board). We enjoyed talking with other travelers as we flew across the Atlantic.
The Oslo airport was a beautiful reflection of the Scandinavian attention to design. We had an incredible view of the stunning Norwegian coastline from the air as we flew to Kirkenes.
Pizza is expensive compared to home — ours was $30! Then again, pizza at home doesn't feature reindeer meat. Gasoline is also quite high compared to North Carolina, averaging $7 a gallon. We have met some of the other participants in this mission and look forward to getting to know the rest of the science party. We will spend the next day getting our things organized and exploring the town of Kirkenes.
—Mike Dunn
Daily Journals | Next >>


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Ive done a little research and found the huawei ascend has the same cpu as some other phones with almost identical specs. Wouldn't that mean the roms are compatible? Thank You in advance.
ROMs for huawei m860 ?
Started by pheenx , Dec 30 2010 01:48 AM
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Name of product:Lion Brand Homespun Yarn
My Review
I belong to a group that knits prayer shawls and lap blankets. Homespun is often used, but I don't like it. It's very hard to knit and splits easily. It can't be used as fringe for the shawls because it unravels. The colors are beautiful, but to me it's not worth the aggrevation.
Would you recommend this to a friend?No
Amy Solovay, About.com Crochet, says:
Thanks for the review, Lynne! I can appreciate what you are saying about Homespun; it is also a challenging yarn to crochet with. I have, however, found that it works wonderfully well for Tunisian crochet. Here's a free bag pattern you could use if you ever want to try that (like maybe if you have any Homespun hanging around in your stash that you wouldn't use otherwise.)


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Honda CB160 Restoration Thread
View Single Post
Scrambler Weirdo
Espresso Racer
Joined: Oct 2010
Location: Somewhere in Ontario
Oddometer: 85
Ok, well I raised the needles again after going ahead and installing the rectifier the other guys were talking about ($12.99 at the electronics store). Bike idles mostly and I have a throttle again. I realized that along with doing the carb top boots I lowered the needles thinking I was running rich, and I was too pissed off over the way the bike ran last night to even realize I was starving it for fuel. Next up is another rewire so I can turn the lights right off with a big toggle to save on the charging system. Old bikes are fun..... Anyways, the rectifier is indeed the same as what the oregon rectifiers are, so it's a cheap and easy upgrade to the charging system. Easy install too, yellow and brown to the AC pins, battery to the positive pin, and just make a ground to the battery for the negative pin. These things are way smaller than our orange ones and you can put them just about anywhere. The one I got is rated for 25A at 400v, should be plenty. Go for it people....
Scrambler Weirdo
View Public Profile
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Miss HerbertHardback
List price $38.94
You save $24.39 62% off
Free delivery worldwide
Dispatched in 5 business days
When will my order arrive?
Additional formats available
- Format
- Paperback $19.66
- Publisher: Jonathan Cape Ltd
- Format: Hardback | 592 pages
- Dimensions: 154mm x 234mm x 52mm | 939g
- Publication date: 25 October 2007
- Publication City/Country: London
- Illustrations note: Illustrations, maps
- Sales rank: 341,284
Product description
The secret history of novelists is often a history of exile and tourism - a history of language learning. Like the story of Gustave Flaubert and Juliet Herbert, it is a history of loss and mistakes. Flaubert's niece was taught by an English governess: Juliet Herbert. As Flaubert finished "Madame Bovary", Miss Herbert translated his novel into English. But this translation has since been lost. No photographs of Miss Herbert survive, either. Translation, and emigration, is the way into a new history of the novel - a history of loss, of mistakes. We assume that we can read novels in translation. We also assume that style does not translate. But the history of the novel is the history of style. "Miss Herbert" solves this conundrum.The book travels from Rio de Janeiro to Prague, from Moscow to London, from Trieste to Paris, from Warsaw to New York. On its zigzagging flight, it reinvents our ideas of style, and translation - introducing new theories of jet lag, of the time difference. "Miss Herbert" finds problems with accurate translations, and praises imperfect ones. It dismisses history and politics, replacing them with the fun of literary games. This is not a novel, but an inside-out novel - with novelists as characters. But "Miss Herbert" is not just a book. It demonstrates a new way of reading internationally. It is a project, a book of tricks - complete with maps, illustrations, and a variety of helpful diagrams. And it comes with a companion, a slim appendix: "Mademoiselle O", a story by Vladimir Nabokov, written in French, about his own governess, never before fully translated into English. "Miss Herbert" is a bedside travel book, a comprehensive city break: the most original and most stylish beach read.
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Author information
Adam Thirlwell was born in 1978. His first novel, Politics, was translated into thirty languages. In 2003, he was chosen as one of Granta's Best British Novelists under forty. He lives in London.


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PTU Date Sheet 2014 March/ April Nov/ Dec BTech BBA BCA BSc MBA MCA MSc- ptu.ac.in:
Punjab Technical University, Jallandhar has been announced the PTU Exam Time Table/ Date Sheet/ Exam Dates Schedule Routine 2014- 15 for B.A, B.Sc, B.Com, B.Ed, M.Sc, M.A, M.Com, M.Ed, M.Phil, BBA, BCA, MBA, MCA Degree Semester & Annual Examination at the Punjab Technical University, Jallandhar official website.
This time, Punjab Technical University, Jallandhar gonna conduct their Semester Exam and annual examinations on March & April and November/ December 2014- 15 and students who are going to write the PTU examinations 2014 can download their Time Table/ Date Sheet from here itself.
Also for the Admission into the various courses offered by them which are categorized into regular private and professional courses, the Private Form, Back paper Examination form have been disclosed. The relative details about the Private Form, Back paper Exam form of B.A, B.Sc, B.Com, B.Ed, M.A, M.Sc, M.Com, M.Ed, BBA, MCA, MBA and various other degree courses.
Punjab Technical University, Jallandhar is expected to display PTU Time Table/ Date Sheet 2014 as soon as possible. Students need to select your name of the course and enter the Roll number or Registration number to see the exam schedule dates by subject and semester wise from the listed below links.
For PTU Time Table/ Date Sheet 2014:
Students having any questions, then send it to us through the comment box or through our official Facebook page.


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You are in North America
|Kevin Hannam
|University of Sunderland
|Dan Knox
|Liverpool John Moores University
|© 2010
|240 pages
|SAGE Publications Ltd
|Sixty Day Exam Copy
|Individual Purchasers
An insightful and original approach to different aspects of tourism...The book is admirable for the interesting, vivid and shrewd style of writing which makes it really enjoyable for reading. Fun and humour are deliberately and successfully interwoven into the elevated academic analysis, thus making this text equally valuable for professionals, academics, students and anyone else who is passionate about tourism
European Journal of Tourism Research
At last! A refreshingly lucid text for students that substantially enriches the analysis of tourism and tourists. Hannam and Knox explore the recent theoretical insights that have helped tourist studies to escape from a self-imposed academic ghetto and have multiplied approaches to making sense of tourism. Clear, concise and stimulating
Tim Edensor
Manchester Metropolitan University
With this book Hannam and Knox have gone a long way towards elevating the study of tourism from the obscure margins of social science into a bona fide research area. They encourage us to think critically about the subject and successfully interweave dominant contemporary concepts to present tourism as a social, cultural, economic, and spatial phenomenon. Students will be sure to enjoy this innovative contribution which takes a 'user-friendly' approach and provides a useful pedagogic tool for those at all levels of study
Dimitri Ioannides
Professor of Human Geography; Mid-Sweden University and ETOUR
Understanding Tourism provides an in-depth and critical analysis of tourism studies that is conceptually rich, empirically strong and extremely accessible to scholars and students of tourism. It is a refreshing analysis of an extremely complex and multidimensional global phenomenon, and raises our understanding of tourism to new heights
Dallen Timothy
Professor of Tourism Development and Management, Arizona State University
A very interesting mobilities view of tourism with useful student-friendly text and exercises
John Urry
Distinguished Professor, Lancaster University
This is a useful and accessible introduction to critical approaches to tourism that will be a value for lecturers and students alike. The provision of many thought-provoking exercises will be of benefit for both teaching and learning
Greg Richards
Annals of Tourism Research
Good reading as an introduction to Travel and Tourism for learners to gain a better understanding of the concept of tourism.
Mrs Alicia Hawkes
Education, Totton College
Oct 16 2013
Report this review
Although the exercises and fact boxes are interesting and reviews each section well and there is a good range of chapter topics I found that the quotes used throughout were quite dated. I would like to see more up to date literature and articles referred to for a 2011 reprint.
Ms Luane Quigley
Hospitality, Tourism & Sport, North West Regional College
Feb 08 2013
Report this review
excellent book for introduction to tourism course
Dr Ashraf Jahmani
department of hotel m, Al-Ahliyya Amman University
Jul 09 2012
Report this review
Very much a theoretical text with the odd case study. Some interesting observations on commodification and past and present trends. The text probably does not have the detail of a Page or Holloway to make it essential reading, but it does provide some useful supplementary material
Dr Paul Fidgeon
Schl of Tourism,Hospitality & Leisure, Thames Valley University
Nov 02 2011
Report this review
Understanding Tourism is a good tool for undergraduate and postgraduate students, introducing an indepth and critical analysis of tourism as a global and fast-changing phenomenon. The book provides a good analysis of the key issues on comtemporary tourism studies, chalenging concepts and definitions.
Mrs Goretti Silva
School of Technology, Viana do Castelo Polytechnic Institute
Apr 01 2011
Report this review
An excellent and well-written text which is clearly written and enables undergraduates to gain an insight into the theoretical aspects underpinning the industry.
Ms Carol Southall
Business School, Staffordshire University
Mar 29 2011
Report this review
Well written and up-to-date. Theoretically well-informed, yet with relevant ethnographic examples. Excercises, suggested readings and a glossary that the students find useful.
Dr Staffan Appelgren
School of Global Studies, University of Gothenburg
Sep 15 2010
Report this review
An extremely accessible text covering a range of fascinating topics which will inspire and motivate students.
Dr Clare Horrocks
Faculty of Media,Arts & Social Science, Liverpool John Moores University
Sep 14 2010
Report this review
A very well writting book which offers interesting insights into tourism. A very useful book for students at any stage of a tourism course.
Mr John Newby
Department of Tourism, Sunderland University
Sep 14 2010
Report this review
This book offers a contemporary insight into tourism and the tourist environment of today. A central feature is the key thinkers and their influential school of thought identified in each of the stuctured chapters. A very good and interetsing read.
Dr Martine Middleton
Dept of Tourism & Leisure Management, Central Lancashire University
Sep 14 2010
Report this review
As more students are taking up Tourism Studies for their careers, there is always the need to have updated textbooks and criticism about the subject. This is a good textbook as it helps to provide good criticism, latest examples, and exercises to enhance each chapter.
Mr Vincent Zammit
Tourism Studies (Tour Guiding, Travel agency Operations), Institute of Tourism Studies
Jun 29 2010
Report this review
With a firm theoretical critique of the defenitional simplifications of much other tourism introductions, it fits our course aims all the way. We also like the excercies and the broad scope of subjects covered. It will replace Bella Dicks, Culture on Display as our main text.
Dr Klas Grinell
Museion, Gothenburg University
Jun 23 2010
Report this review
The book contains most specific issues and scientific disciplines around tourism, integrating them with a holistic view. Because of this, this book differs from standard tourism text books giving an overview. As I start to teach an introduction course in autumn, I am very glad to have found this book which gives an very good overview and quite a solid basic knowledge.
Dr Harald Friedl
Healt Management in Tourism, University of Applied Science
May 21 2010
Report this review
Very interesting (have not read all yet). Might even be essensial reading.
Dr Oystein Normann
Dept of Travel & Tourism, Harstad University College
Apr 08 2010
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Not complaining but I'm curious why this got moved since the my Llama is a 1911 design. It seemed like the correct forum for the post as there were other posts related to the weapon already present there.
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The Brother Basil DLX is the enhanced version of Royal Elastics' classic Brother Basil shoe.
A deconstructed, remixed Chukka boot, the Brother Basil is composed of a black denim upper, a luxurious pigskin lining and Royal Elastics' signature Stretch-fit Closure system—which makes sliding in and out of these shoes a breeze. And these durable, beautiful boots feature an ultra-light bottom unit that includes a molded footbed, an EVA midsole and a Vulc sole with a heel stripe for extra pop.
Founded in 1996, Royal Elastics is dedicated to creating high-quality, extra-comfortable men's and women's shoes for every place and occasion.
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JoeZ1116: Quiz Results
Do You Know Your 10-Codes? taken about 4 years ago
0-50% correct
How Do You Handle Danger? taken over 5 years ago
You handle danger with Courage
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"The 10 codes aren't part of the EMT Training, I hear them all the time on the scanner while on-duty and that's it!"
"Thank you kindly for the St Michael's Coin! That is a cool cube of Insignia, I understand it since my father, a retired PO also except from the NY..."
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My week is going pretty well so far and I hope yours is too.Take care.
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The 10 codes aren't part of the EMT Training, I hear them all the time on the scanner while on-duty and that's it!
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Philosophy is more complex than Neurology, or try Christology. :)
The temperature here today is supposed to be 43 degrees not so warm when you have 30 mph winds.
I don't care what Punxsutawney Phil says by my calendar we still have six more weeks until Spring.
Happy Groundhog Day from Punxsutawney!
Phil Says Expect an Early Spring!
Phil's official forecast as read February 2nd, 2011, at sunrise at Gobbler's Knob in Punxsutawney, PA:
Here Ye, Hear Ye, Hear Ye
Groundhog Day, February 2, 2011
Punxsutawney Phil was raised from his burrow
By the call of President Bill Deeley.
He greeted his handlers, Ben Hughes and John Griffiths.
After casting an inquisitive eye towards thousands of his faithful followers,
He proclaimed that the Steelers are going to the Super Bowl!
Back to the business at hand...
He surveyed his surroundings carefully and found that there was no shadow around,
So, an early spring it will be.
Note: In order to help handle the enormous amount of traffic on the web site, we have temporarily trimmed the site to a bare bones, low-bandwidth version. Please visit us again for the full version of our site, with news and other fun features about Punxsutawney and its most famous resident! Oh, and GO STEELERS!
over 4 years ago
20164 Comments
Thanks for the friendship! How's things in your neck of the woods? Hope your enjoying your weekend and have a great week ahead! I haven't been on here much lately as I've been getting over some bug that has been kicking my behind. We all seemed to have had it in one form or another. It.s been dreary here the last few days and it's raining now in the high 50's, got all excited as it was sunny and in the 80's last week Guesss I got spoiled,what happened to sunny Calif? Now my heater just went out again and I just got it fixed, brrrrr. Take care and stay safe out there as the crazies walk among us.


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Emmett ,Id
Joined: Mar 2007
Oddometer: 184
This is how Ryan gets firewood
Long time Idaho rider
Joined: Jun 2008
Location: Boise, Idaho, USA
Oddometer: 670
Looks like a super trip, Ryan, Phil, Wurty! I'm sitting in Moscow right now, having covered some of that same country bringing my daughter up to college orientation the "scenic" way this last weekend. We ran into plenty of snow, same as you. Made it through some and gave up a couple times. A pain but damn, the ridges, valleys, meadows are just gorgeous with water and wildflowers.
Set Adrift
Joined: May 2006
Location: Back in the Saddle
Oddometer: 4,147
I have a ride to the KLIM RALLY Started over here
My Ride South of the Border
Riding Nevada's Pony Express Trail May 2013
To travel is to discover that everyone is wrong about other countries.
Aldous Huxley
pavement inspecter
Joined: Sep 2006
Location: Southern Idaho
Oddometer: 307
Great pictures and report Ryan.
Wow, Ryan you guys had some GREAT riding and FUN for sure. I picked up a 2004 DRZ400 a couple of weeks ago. It has 1700 miles on it and it was as near STOCK as one can get. MINT condition for 2600.00
I hope to get out this year more as the past two years have been VERY PAINFUL (no detail here).
Thanks again for sharing your ride.
Studly Adventurer
Joined: Apr 2008
Location: United States
Oddometer: 855
Boise Lodging?
Looking for a relatively inexpensive place to stay for about a month beginning next week. Someone suggested posting in this thread to get more replies. Camping is OK. Will need commutable distance to Boise and showers. All suggestions are appreciated.
Long time Idaho rider
Joined: Jun 2008
Location: Boise, Idaho, USA
Oddometer: 670
RR: Some Danskin with the boy
I am just not feeling it yet. Oh sure, theres the wind, the blue sky, the rumble of the boxer engine below, but heading down the road to the mountains with Hunter on board, I might as well be sitting in the office chair at work for how excited I am.
Our plan to go on a longer ride before Hunter travels to his dads for the summer has been repeatedly postponed by rain, graduation events and birthday parties. Such is life with the four kids. Today is our last chance. Hunters plane departs at 6:10.
We cut a few miles through town and join the old path of the Oregon Trail behind the Micron Technology campus here in Boise. The primitive path is usually rough but an exceptionally wet spring has added ruts and puddles.
Ready for the dirt, Hunter? I ask with pep-talk enthusiasm, as much for myself as him. I expect the demands and delights of the trail will rouse the senses.
Yeah, he deadpans. We seem to be in the same mood.
We are making a spirited ascent of a rocky hill, weaving around obstacles, when I notice a couple with a chocolate lab and wide rimmed hats standing at the edge of the trail ahead. The lady is giving us the eye. I slow down, offer a friendly nod and wave as we pass. They wave backfriends made, lost and reconciled in thirty seconds.
Stand there a sec, I ask as Hunter gets off the motorcycle in the the large gravel lot at Bonneville Point. He scowls and sulks as I square up for a photo. I take the shot then put my hand on his armored shoulder.
You doing okay, Hunter?
Yeah, he answers without looking up.
This is your ride, buddy. Tell me if you want to do some other kinds of stuff.
Bonneville Point
He says okay but nothing more. He begs to ride so Im surprised hes sullen. Maybe its about leaving. Transitioning between homes hasnt bothered him much beforehe kind of lives in the momentbut that could be changing as he gets older. Hes excited to see his dad but the friends, family and other things here are a growing part of his life that will be left behind.
I remember as a kid when grown-ups asked how I felt, was everything okay, it usually just irritated me. I wasnt self-aware. I didnt know and I wasnt interested in thinking about it. I imagine that might be Hunters perspective. Rather than press him to explain his mood I think well just do our best to enjoy the day.
Remember that tree with the huge thorns? I ask as I begin walking down the concrete path toward the gazebo. I think its right over here somewhere.
Here it is! he announces.
I know he enjoys facts so I tell him, This is a locust tree. The thorns are so strong that people have used them for nails. Hunter makes a lengthy examination of the thorns while I look around at the lupine and other flowers growing here.
Looking out over Boise
You ready to go? I ask. Were gonna be on some cool trails pretty soon. I think youll like it.
I have plotted a route that will take us from the Willow Creek Trailhead back to the Bender Creek Trailhead in the Danskin OHV area. We wind around imposing outcrops as we follow the gravel road along Wood Creek to our first trailhead. I breathe in the smell of coniferous trees that grow along the burbling ribbon of water here in the shade of the canyon. Its invigorating.
We pass by the trailhead for a quick look from the bench above the South Fork of the Boise River, just ahead. As the view opens before us, two military helicopters fly nap-of-the-earth from across the water then over us.
Cool! Hunter yells. Those are army helicopters. You know how I can tell? he asks. By the color. He answers himself before I can offer my guess. I enjoy how excited he is.
North Fork of the Boise River
We stop for a few pictures of the blue river curving through the green canyon toward white-capped mountains then return to hike a small area matted yellow with wildflowers. Colors are brilliant today.
We park off the side of the road and begin to walk through a profusion of arrowleaf balsamroot. A lady appears ahead walking toward us over a small rise, her shape and gait that of someone more accustomed to the couch. Two large cameras hang from straps around her neck, one behind, one in front.
Two more back there, she says, short of breath. Just wanted to let you know.
Okay, thanks, I answer. Im unsure of her thinking so add, well just be walking, thoughnot gonna ride. We crest the rise ourselves and there meet who I take to be her husband and son.
You going to see the eagles? the husband asks. I pause long enough for him to realize I dont know what hes talking about. Well, just go all the way out to the point and look down, he explains. Theres a nest.
In a U-shaped tree, the son adds excitedly.
Right, the man confirms even before his son finishes, U-shaped, just below the cliff. The bright blue BSU football T-shirt stretched tightly across his expanding gut is emblematic of his enthusiasm.
Thanks, really appreciate it, I tell them as we turn and continue walking. We check along the cliff edge and finally at the rocky point, just as described for us, we spot the nest well below. We see movement but cant make out any details from this distance.
Can we walk out there? Hunter implores, pointing to a rocky spire some fifty yards farther out.
I dont think so, Hunter. That would take a while. What he calls a hike would really be a lot of climbing and scrambling, down then back up.
Please, he begs. Im really fast on rocks.
I check my watch again. Id love to Hunter but we need to be home for your flight. Sorry about that. Well climb out there next time were here.
I am just glad hes finding some excitement. We walk in silence a few minute back toward the motorcycle when he suddenly announces, Im gonna tell my teacher about what I saw!
Has he seen something I missed? The eagles and army helicopters? I ask.
Before I can remind him that hes out of school he explains, Im gonna visit Mrs. Schweitzer, his fourth grade teacher. I wonder how he plans to do that but think Ill just let him enjoy the idea.
On the motorcycle again, we descend from the bench back to Willow Creek and turn into the head of Danskin Trail 400. The way is wide and well marked. This looks easy.
Then we come to the creek. The water in the middle is a darker green, suggesting some depth. I cant tell how deep, though. It makes me nervous. I climb a bit up the hill on this side to see farther up the trail, judge whether its worth it. It looks nice enough.
There is some risk of mishap but the creek isnt that wide and I think it will do Hunter and I good to contend with something outside ourselves today.
Hey Hunter, grab your helmet and walk up there, I point upstream. Youll be able to cross over on some rocks. I dont want him on board if I cant make it.
He grabs his helmet and takes off. I grab a handful of throttle and hope for the best. The bike sputters as it plunges and tries to climb the opposite bank. Even hard on the throttle it barely makes it. It leaves me uneasy.
I park, walk to the creek, straddle some boulders and extend my hand to help Hunter jump across. Im glad to have that behind us. Now we can have a pleasant ride through the trees up to the ridge.
Or not. We arent far down the trail before we see it doesnt climb the ridge. At least not here. Instead it dumps us back at the creek for an even larger water crossing. I stare a moment at the water. I hear Hunter say something about how we can cross it but I dont really listen. This is too much.
I help Hunter back across the rocks and walk with him down to the first water crossing. One way or another, I expect this to be interesting. Id like you to take some pictures, Hunter. The lens is manual so I pre-focus, set it to f/11 and hand the camera to him. Just point that way and push this button a bunch.
Okay. Hes excited for the job. Im not. I bet I could cross it on a dirt bike, he tells me as I begin to walk away.
I turn back and smile. Yeah, youre probably right. Its good to be optimistic.
I hustle back up to the bike, get on and get pointed in a good direction near the waters edge. Part of me wants to out-think this but theres really nothing to think about. Just go!
I realize Im sunk when the bike starts to sputter while still in deep water well away from the other edge. It loses power then dies. Darn. I step off into water above my knees and feel the cold rush into my boots.
Jason, youre blinker is on! Hunter yells. When I dont answer he yells again more urgently. Im short on humor at the moment and want to yell back, forget the stupid blinker.
Thanks Hunter, I manage to answer. Just keep taking pictures, okay?
Earlier we saw a rough looking couple pull up in what looked like an old Datsun and begin setting up camp below. I think about having Hunter run down to ask for help but decide to see what I can do first.
I dig the edges of my boots into the underwater sand and push. The bike moves along easier than I expected! Maybe its half floating. Im able to get most of the engine up out of the water before I need to rest.
I need to continue but its steeper and the sand is just sliding underfoot now. Before going for help I give a what-the-hell push on the starter button. Its rough but it starts! I rev, pop the clutch and push. Sand and water churn between my legs as the bike slowly climbs out.
While Hunter is running around with the camera chasing butterflies, I pour the water out of my boots and begin removing panels. In twenty or thirty minutes, with a dried airbox and filter, the bike is running normally again.
We still have a little time to ride trails. There are several trucks at the Bender Creek trailhead down the road, what was to be our exit. At least one little barbecue is underway in the parking lot. Other people are sitting on their tailgates. As we cross a small bridge and begin climbing the trail I feel like we have an audience.
After a little time on the trail, I ask, you having fun with this?
Yeah, he answers sincerely. After a pause he continues, its kind of scary when you go fast up hills.
Sometimes we have to go a little bit fast just to be sure we make it, I explain. I think about explaining how on these very trails his mom ended up with a broken elbow and facial lacerations after I took a sharply canted switchback too slow. That might alarm him, though, so I leave it at that.
After snaking around ridges and running a stretch through a riparian ravine, we stop for a break on a hill that provides views all around. Hunter focuses on finding pretty rocks while I go for a drink from the flexible canteen. Something squirts me. What? I hold up the canteen and see the clean, round puncture.
That shouldnt happen. Theres nothing sharp back here. Then I see in the motorcycle bag the cluster of several-inch-long locust thorns Hunter must have tossed in for a souvenir. Beneath that, an inch of water on the air pump and electrical adapters I carry. Darn.
I hold up the thorns. Hunter, you cant put things like this into the bag. I take care to keep a casual tone so I dont detract from his day. You need to ask before you put anything in here.
Okay, he acknowledges sheepishly.
I need you to hold this upside-down so it doesnt leak while I dry things off. I hand him the canteen. Then well have to take our last drinks and dump it out.
Rags, cables and gadgets are spread out on the motorcycle to dry while Hunter and I have some trail mix and a look around. He collects a few rocks that I tuck safely into a back pocket of the bag.
South across the Snake River Plain to the Owyhees
Things are still damp but our schedule encourages us onward.
I remember disliking this route but forgot how much. Danskin Trail 500 is a lot of sand and waterbars, a slow beating as we make our way back to the road. I am glad for the beautiful views and pleasant weather.
To make sure were home in time, I ramp onto the freeway for the few miles back to Boise. The part of the ride I like least seems to be one of Hunters favorites. Hes surfing his hands through the wind and pumping his fist at every big rig hoping theyll honk. Thats the Hunter we know and love.
It has been a good ride. The little trail challenges were a good experience, memories to enjoy, and just what we needed to spin free of the languid place we were mired in when the day began. Good bye for the summer, little man.
Jason Abbott screwed with this post 07-28-2011 at 10:01 AM
Muck Savage
Joined: Jan 2006
Location: Dubai, UAE
Oddometer: 150
What a lovely story and ride report. Thanks so much for sharing Jason.
Why keep a dog and bark yourself ?
2007 BMW G 650 X Challenge
Get Out and Ride!!
Joined: Dec 2006
Location: Nampa, Idaho
Oddometer: 3,861
Great pics, Jason. I've never taken my bike out there... and keep telling myself I will. I need to get around to that ~ those trails look excellent.
Ride your own ride & enjoy your ride.
Studly Adventurer
Joined: Jan 2007
Location: Boise Idaho
Oddometer: 665
Taking A Beemer up Willow..... now that would have been an adventure.....
2006 DRZ 400 E / Plated - 2012 Yamaha Super Tenere
OBR ADV Gear
Website - www.obradvgear.com
Facebook - OBR ADV Gear
Long time Idaho rider
Joined: Jun 2008
Location: Boise, Idaho, USA
Oddometer: 670
Studly Adventurer
Joined: Jan 2007
Location: Boise Idaho
Oddometer: 665
You could have taken 410 which headed up the hill to the left. 410 runs parallel up on the hill with Willow. 410 then connects to 317 and then into 300 which heads back into Bender Crk. 317 to the east off of 410 takes you into Fiddler Flat, which I would recommend. These routes aren't difficult, 300/317 are all ATV tracks the same as 500.
2006 DRZ 400 E / Plated - 2012 Yamaha Super Tenere
OBR ADV Gear
Website - www.obradvgear.com
Facebook - OBR ADV Gear
Long time Idaho rider
Joined: Jun 2008
Location: Boise, Idaho, USA
Oddometer: 670
Joined: Apr 2009
Location: Idaho
Oddometer: 30
Anybody want to meet up for a ride?
Or is anybody planning a ride I can tag along on?
Risk Taker
Joined: Apr 2010
Location: Boise, ID
Oddometer: 1,144
Flying home to Boise for a short break from Denver today. After putting money down in mid-Feb, waiting til early May to actually see it, only having enough time to put 160 miles on it, then leave it with Happy Trails for six weeks, The Triumph will finally be in my possession!! Riding her back to Denver on Thursday/Friday. Tking the road less traveled. No dirt due to time constraints to get back to Denver, but riding on all two lane from SLC to Denver. Going to Pick up 35 in UT South of SLC, head to Dinosaur on 40, South to Rangely, then Meeker, CO 8 to Yampa, CO, 131 South to 134, and pick up 40 again. Depending on time, I may take 40 through Winter Park and over Berthoud, or I may just run 9 South and pick up the interstate the last 85 miles to Denver. Will be a great trip on my new bike! Hope y'all are finallly getting some good weather back there!
2011 Triumph 800 XC
2007 Honda CRF 250X
1994 Kawasaki KLX 650R
THE BACKCOUNTRY PURSUIT- Boise, Idaho's consignment specialist for ADV gear!
Set Adrift
Joined: May 2006
Location: Back in the Saddle
Oddometer: 4,147
Just returned home and read your day ride in the Danskins; you never cease to amaze me with your wonderful insight and commanding gift of the written word. I will say this though.... you sir are nuts, for the places you take that german two wheeled Panzer but I must applaud you on those endeavors as you always manage to emerge unscarred not to mention relatively intact.
See you out there
My Ride South of the Border
Riding Nevada's Pony Express Trail May 2013
To travel is to discover that everyone is wrong about other countries.
Aldous Huxley
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Lines About Squares - Western Square Dancing
In this article, part of his long-running column, the author looks at the typical programs of Western square dancing in the late 1940s and early 1950s. He discusses the different kinds of patter, mentioned the predominance of singing calls at this time, and looks in depth at Rickey Holden's "Star By the Right."
The Girl I Left Behind Me (clip) - Lee Bedford, Jr.
In his brief look at the development of singing calls, Tony Parkes cites the publication of this dance in 1928 as "the earliest description of a singing square I've found so far (in fairly shallow digging)." This SDHP website includes an 1893 reference, plus other early mentions of the dance.
Cowboy Loop (clip) - Lee Bedford, jr.
This dance was called by Mildred Blakey at the big 1950 Santa Monica dance.
Tags: Cowboy Loop, Lee Bedford Jr., Texas
Arkansas Traveler (clip) - Lee Bedford, Jr.
View full record for details.
Tags: Arkansas Traveler, Lee Bedford Jr., Texas
Four In Line You Travel (clip) - Lee Bedford, Jr.
View full record for details.
Square Dances With Calls - Lee Bedford, Jr.
In 1949, Texas caller Lee Bedford released on Imperial Records a four-album set of recordings with music provided by The Big D Ranch Hands. The liner notes, written by Paul Erfer, start by noting, "The interpretation of the figures described follows the style of square dancing as dances in some parts of Texas."Each record had a patter call on the A…
Tags: Lee Bedford Jr., Texas
Uptown – Downtown (Golden Slippers) - Ed Durlacher
Classic square dance figure, Uptown Downtown, done as a singing square to Golden Slippers by caller Ed Durlacher; music provided by The Top Hands, directed by Frank Novak. One of the Related Items is a newsreel with Durlacher calling this very dance in Central Park, New York. More detailed information about this recording, part of a collection,…
Tags: singing square
Smoke On The Water, introduced by Ed Gilmore
During a morning workshop at the 1954 Minnesota State Convention Ed Gilmore introduces a "new" singing call written by his friend Pancho Baird.Tony Parkes comments:===It may have been new, but Ed had clearly studied it and made it his own; he changed some word metering, as he often did, to give the actual commands earlier and keep the dancers…
East Is East - Pat Pending
Pat Pending was the pen name under which Ed Moody contributed numerous poems to Ralph Page's magazine, Northern Junket. In this one, the poet looks at two distinct styles of dance calling and implores callers not to mix them.
Tags: Ed Moody, humor, Pat Pending, poem
Ed Gilmore Teaching Dance Style
This is an audio recording of Ed Gilmore calling a morning workshop at the Minnesota State Convention in 1954. His subject is dancing style. At about 7 minutes he starts a teach of the figure Balance Eight.
Tags: Balance Eight, Ed Gilmore, Style, styling
Four Bachelor Boys - Richard Kraus
Let's Square Dance!, Album 5
Swing Like Thunder - Richard Kraus
Kraus writes, "This lively square dance is especially popular with teen-agers." In his book, Square Dances of Today, he writes, "This one goes under a variety of names. Some call it the 'California Fruit Basket' and others call it 'Ladies Bow, Gents Bow Under.' "Let's Square Dance!, Album 4
Lady Go Halfway Round - Richard Kraus
Kraus says, "This is not a difficult square, but for a few moments the active boy has to keep his ears open, and do some fast stepping!"
Let's Square Dance!, Album 3
Let's Square Dance!, Album 3
Coming 'Round the Mountain - Richard Kraus
Let's Square Dance, Album 3
Swing at the Wall - Richard Kraus
Let's Square Dance!, Album 2
Form an Arch - Richard Kraus
Let's Square Dance!, Album 2
Red River Valley - Richard Kraus
Let's Square Dance!, Album 1
Duck for the Oyster - Richard Kraus
Let's Square Dance!, Album 1
Let's Square Dance! - instruction booklet - Richard Kraus
This a sample instruction booklet from Album 3 in the "Let's Square Dance!" series, aimed at ages 12-14, Grades 7-8.
Let's Square Dance! - Richard Kraus
This series of five albums was recorded in 1956 featuring the calling of Richard Kraus, a caller and professor at Teachers College, Columbia University. This item serves as a general introduction to the series, including the table of contents showing how dances were arranged by age / grade level. Subsequent items will present clips from different…