dorsal/arxiv
View SchemaBateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator
| Authors | Massimo Blasone, Petr Jizba |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0102128 |
| URL | https://arxiv.org/abs/quant-ph/0102128 |
| DOI | 10.1016/j.aop.2004.01.008 |
| Journal | Annals Phys.312:354-397,2004 |
Abstract
By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a system are constructed and discussed entirely in the framework of the classical theory. The corresponding geometric (Pancharatnam) phase is calculated and found to be directly related to the ground-state energy of the 1D linear harmonic oscillator to which the 2D system reduces under appropriate constraint.
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"abstract": "By using the Feynman-Hibbs prescription for the evolution amplitude, we\nquantize the system of a damped harmonic oscillator coupled to its\ntime-reversed image, known as Bateman\u0027s dual system.\n The time-dependent quantum states of such a system are constructed and\ndiscussed entirely in the framework of the classical theory.\n The corresponding geometric (Pancharatnam) phase is calculated and found to\nbe directly related to the ground-state energy of the 1D linear harmonic\noscillator to which the 2D system reduces under appropriate constraint.",
"arxiv_id": "quant-ph/0102128",
"authors": [
"Massimo Blasone",
"Petr Jizba"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1016/j.aop.2004.01.008",
"journal_ref": "Annals Phys.312:354-397,2004",
"title": "Bateman\u0027s dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator",
"url": "https://arxiv.org/abs/quant-ph/0102128"
},
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