ACCURACY OF SEMICLASSICAL METHODS FOR SHAPE-INVARIANT POTENTIALS

We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exa ctly solvable shape-invariant potentials. For these potentials, the gr oundstate energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification, usi ng nonintegral Maslov indices, is substantially better, and the supers ymmetric WKB quantization method gives exact answers for all energy le vels.