From Feynman’s path integral, we derive quasiclassical quantization rules in supersymmetric (SUSY) quantum mechanics. First, we derive a SUSY counterpart of Gutzwiller’s formula, from which we obtain the quantization rule of Comtet, Bandrauk, and Campbell [Phys. Lett. B 150, 159 (1985)] when SUSY is a good symmetry. When SUSY is broken, we arrive at a quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken-SUSY cases. Insofar as broken-SUSY cases are concerned, there are strong indications that the new quasiclassical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.

• Received 3 August 1994

DOI:https://doi.org/10.1103/PhysRevA.50.3638