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 exactly solvable shape invariant potentials. For these potentials, the ground state energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification using nonintegral Maslov indices is substantially better, and the supersymmetric WKB quantization method gives exact answers for all energy levels.