QUASI-CLASSICAL PATH-INTEGRAL APPROACH TO SUPERSYMMETRIC QUANTUM-MECHANICS

From Feynman's path integral, we derive quasiclassical quantization ru les in supersymmetric (SUSY) quantum mechanics. First, we derive a SUS Y counterpart of Gutzwiller's formula, from which we obtain the quanti zation rule of Comtet, Bandrauk, and Campbell [Phys. Lett. B 150, 159 (1985)] when SUSY is a good symmetry. When SUSY is broken, we arrive a t a quantitation formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain o ne-dimensional bound state problems. The wave functions in the station ary phase approximation are also derived for SUSY and broken-SUSY case s. Insofar as broken-SUSY cases are concerned, there are strong indica tions that the new quasiclassical approximation formula always overest imates the energy eigenvalues while WKB always underestimates.