  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.
