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Quasi-classical path integral approach to supersymmetric quantum mechanics

Akira Inomata·Georg Junker
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Abstract

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new 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 a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.

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Akira Inomata, Georg Junker. 1994-08-19. Quasi-classical path integral approach to supersymmetric quantum mechanics. https://doi.org/10.1103/physreva.50.3638

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