Quasi-classical path integral approach to supersymmetric quantum mechanics

Details Quasi-classical path integral approach to supersymmetric quantum mechanics Quasi-classical path integral approach to supersymmetric quantum mechanics

1994-08-19

arxiv.org/abs/cond-mat/9408054v1

Phys. Rev. A 50 (1994) 3638-3649

Physics

Condensed Matter

13 pages + 5 figures, complete paper submitted as postscript file, to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.50.3638

{}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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