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International Journal of Modern Physics A

THE HAMILTON – JACOBI TREATMENT OF SUPERSYMMETRIC QUANTUM MECHANICS

Dumitru Bǎleanu, Yurdahan Güler

Published May 20, 2001• 10 citations
Publisher

Abstract

We study the Hamilton–Jacobi quantization of supersymmetric quantum mechanics. The equations of motion of the Grassmann variables are obtained from the integrability conditions. The results are in agreement with those obtained by Dirac's procedure.
DOI
10.1142/s0217751x01004207

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It is well known in classical mechanics that the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. Analogously, the equivalent quantum action variable appearing in the quantum Hamilton–Jacobi formalism can provide the energy eigenvalues of a bound state problem, without the necessity of solving the corresponding Schrödinger equation explicitly. This elegant and useful method is elucidated here in the context of some known and not so well-known solvable potentials. It is also shown how this method provides an understanding as to why approximate quantization schemes such as ordinary and supersymmetric WKB can give exact answers for certain potentials.
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