Quantum Hamilton-Jacobi formalism and the bound state spectra

Details Quantum Hamilton-Jacobi formalism and the bound state spectra Quantum Hamilton-Jacobi formalism and the bound state spectra

1995-12-14

arxiv.org/abs/quant-ph/9512018v2

Physics

Quantum Physics

20 pages, latex, 5 Figures available on request. This paper arrived incomplete at the archive, and is now repaired.

Scientific paper

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. The equivalent quantum action variable appearing in the quantum Hamilton-Jacobi formalism, can, analogously provide the energy eigenvalues of a bound state problem, without having to solve the corresponding Schr\"odinger 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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