J. Phys. II France 1 (1991) 97-121
Semiclassical matrix-mechanics. II. Angular momentum operatorsRichard M. More
Lawrence Livermore National Laboratory L-321, Livermore, CA 94550, U.S.A.
(Received 27 June 1990, accepted in final form 29 October 1990)
Semiclassical angular momentum matrices are calculated using a new contour-integral formula for matrix-elements. WKB spherical harmonic functions are found to be exaclty orthonormal with the contour-integral inner-product. Matrix-elements obtained from these wave-functions are accurate to about 2 % and the matrices obey the commutation relations expected of quantum angular momentum operators. The semiclassical wave-functions are related to a superposition of allowed classical orbits and this illustrates the connection to the Feynman pathsummation formulation of quantum mechanics for electrons in a spherically symmetric potential.
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