SEMICLASSICAL MATRIX-MECHANICS .2. ANGULAR-MOMENTUM OPERATORS

Semiclassical angular momentum matrices are calculated using a new contour-integral formula for matrix-elements. WKB spherical harmonic functions are found to be exactly 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 path-summation formulation of quantum mechanics for electrons in a spherically symmetric potential.