Note on the Orbital Angular Momentum Eigenvalues

Dipankar Home, S. Sengupta

Eugen Merzbacher

H. A. Buchdahl

That the eigenvalues of the components of orbital angular momentum are integral is most often inferred from the requirement that the Schrödinger representatives of the angular momentum eigenkets shall be single-valued functions of the spatial coordinates. Physical interpretation, however, requires only that the squared modulus of any wavefunction shall be single-valued, which leads only to the weaker conclusion that the eigenvalues are either all integral or all half-odd integral. It is shown here in an elementary manner that the eigenvalues are in fact integral, any explicit appeal to single-valuedness being avoided.

C. G. Gray

S. J. van Enk, Gerard Nienhuis

We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of S z and L z. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.

Brian P. Anderson