Shape invariant potentials in SUSY quantum mechanics and periodic orbit theory

Abstract

We examine shape invariant potentials (excluding those that are obtained by scaling) in supersymmetric quantum mechanics from the stand-point of periodic orbit theory. An exact trace formula for the quantum spectra of such potentials is derived. Based on this result, and Barclay's functional relationship for such potentials, we present a new derivation of the result that the lowest order SWKB quantisation rule is exact.

4 pages, 1 figure, corrected typos, minor revisions, added references