the other. For example, in spin–orbit coupling, angular momentum can transfer between L and S, but only the total J = L + S is conserved. In another example, in an atom with two electrons, each has its own angular momentum J1 and J2, but only the total J = J1 + J2 is conserved. In these situations, it is often useful to know the relationship between, on the one hand, states where all have definite values, and on the other hand, states where all have definite values, as the latter four are usually conserved (constants of motion). The procedure to go back and forth between these bases is to use Clebsch–Gordan coefficients. One important result in this field is that a relationship between the quantum numbers for : For an atom or molecule with J = L + S, the term symbol gives the quantum numbers associated with the operators . Orbital angular momentum in spherical coordinates Angular momentum operators usually occur when solving a problem with spherical symmetry in spherical coordinates. The angular momentum in the spatial representation is In spherical coordinates the angular part of the Laplace operator can be expressed by the angular momentum. This leads to the relation When solving to find eigenstates of the operator , we obtain the following where are the spherical harmonics. See also Runge–Lenz vector (used to describe the shape and orientation of bodies in orbit) Holstein–Primakoff transformation Jordan map (Schwinger's bosonic model of angular momentum) Vector model of the atom Pauli–Lubanski pseudovector Angular momentum diagrams (quantum mechanics) Spherical basis Tensor operator Orbital magnetization Orbital angular momentum of free electrons Orbital angular momentum of light Notes References Further reading Quantum Mechanics Demystified, D. McMahon, Mc Graw Hill (USA), 2006, Quantum mechanics, E. Zaarur, Y. Peleg, R. Pnini, Schaum's Easy Outlines Crash Course, Mc Graw Hill (USA), 2006, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd Edition), R. Eisberg, R. Resnick, John Wiley & Sons, 1985, Quantum Mechanics, E. Abers, Pearson Ed., Addison Wesley, Prentice Hall Inc, 2004, Physics of Atoms and Molecules, B.H. Bransden, C.J.Joachain, Longman, 1983, Angular Momentum. Understanding Spatial Aspects in Chemistry and Physics, R. N. Zare, Wiley-Interscience, 1991, Angular momentum Quantum mechanics Rotational symmetry