of the box, we can rewrite the spacial part of the wave function succinctly as: Momentum wave function The momentum wavefunction is proportional to the Fourier transform of the position wavefunction. With (note that the parameter describing the momentum wavefunction below is not exactly the special above, linked to the energy eigenvalues), the momentum wavefunction is given by where sinc is the cardinal sine sinc function, . For the centered box (), the solution is real and particularly simple, since the phase factor on the right reduces to unity. (With care, it can be written as an even function of .) It can be seen that the momentum spectrum in this wave packet is continuous, and one may conclude that for the energy state described by the wavenumber , the momentum can, when measured, also attain other values beyond . Hence, it also appears that, since the energy is for the nth eigenstate, the relation does not strictly hold for the measured momentum ; the energy eigenstate is not a momentum eigenstate, and, in fact, not even a superposition of two momentum eigenstates, as one might be tempted to imagine from equation () above: peculiarly, it has no well-defined momentum before measurement! Position and momentum probability distributions In classic physics, the particle can be detected anywhere in the box with equal probability. In quantum mechanics, however, the probability density for finding a particle at a given position is derived from the wavefunction as For the particle in a box, the probability density for finding the particle at a given position depends upon its state, and is given by Thus, for any value of n greater than one, there are regions within the box for which , indicating that spatial nodes exist at which the particle cannot be found. In quantum mechanics, the average, or expectation value of the position of a particle is given by For the steady state particle in a box, it can be shown that the average position is always , regardless of the state of the particle. For a superposition of states, the expectation value of the position will change based on the cross term which is proportional to . The variance in the position is a measure of the uncertainty in position of the particle: The probability density for finding a particle with a given momentum is derived from the wavefunction as . As with