dorsal/arxiv
View SchemaQuantum Hamilton-Jacobi formalism and the bound state spectra
| Authors | R. S. Bhalla, A. K. Kapoor, P. K. Panigrahi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9512018 |
| URL | https://arxiv.org/abs/quant-ph/9512018 |
Abstract
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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"abstract": "It is well known in classical mechanics that, the frequencies of a periodic\nsystem can be obtained rather easily through the action variable, without\ncompletely solving the equation of motion. The equivalent quantum action\nvariable appearing in the quantum Hamilton-Jacobi formalism, can, analogously\nprovide the energy eigenvalues of a bound state problem, without having to\nsolve the corresponding Schr\\\"odinger equation explicitly. This elegant and\nuseful method is elucidated here in the context of some known and not so well\nknown solvable potentials. It is also shown, how this method provides an\nunderstanding, as to why approximate quantization schemes such as ordinary and\nsupersymmetric WKB, can give exact answers for certain potentials.",
"arxiv_id": "quant-ph/9512018",
"authors": [
"R. S. Bhalla",
"A. K. Kapoor",
"P. K. Panigrahi"
],
"categories": [
"quant-ph"
],
"title": "Quantum Hamilton-Jacobi formalism and the bound state spectra",
"url": "https://arxiv.org/abs/quant-ph/9512018"
},
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