dorsal/arxiv
View SchemaClassical and quantum mechanics of a particle on a rotating loop
| Authors | Sayan Kar, Avinash Khare |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9904083 |
| URL | https://arxiv.org/abs/quant-ph/9904083 |
| DOI | 10.1119/1.1286427 |
| Journal | Am.J.Phys. 68 (2000) 1128-1133 |
Abstract
The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics from both exact and semi--classical standpoints. Exact solutions of the Schrodinger equation are obtained in some cases by diverse methods. Instantons, bounces are constructed and semi-classical, leading order tunneling amplitudes/decay rates are written down. We also investigate qualitatively the nature of small oscillations about the kink/bounce solutions. Finally, the connections of these toy examples with field theoretic and statistical mechanical models of relevance are pointed out.
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"abstract": "The toy model of a particle on a vertical rotating circle in the presence of\nuniform gravitational/ magnetic fields is explored in detail. After an analysis\nof the classical mechanics of the problem we then discuss the quantum mechanics\nfrom both exact and semi--classical standpoints. Exact solutions of the\nSchrodinger equation are obtained in some cases by diverse methods. Instantons,\nbounces are constructed and semi-classical, leading order tunneling\namplitudes/decay rates are written down. We also investigate qualitatively the\nnature of small oscillations about the kink/bounce solutions. Finally, the\nconnections of these toy examples with field theoretic and statistical\nmechanical models of relevance are pointed out.",
"arxiv_id": "quant-ph/9904083",
"authors": [
"Sayan Kar",
"Avinash Khare"
],
"categories": [
"quant-ph"
],
"doi": "10.1119/1.1286427",
"journal_ref": "Am.J.Phys. 68 (2000) 1128-1133",
"title": "Classical and quantum mechanics of a particle on a rotating loop",
"url": "https://arxiv.org/abs/quant-ph/9904083"
},
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