dorsal/arxiv
View SchemaA unified approach to exact solutions of time-dependent Lie-algebraic quantum systems
| Authors | Jian Qi Shen, Hong Yi Zhu, Pan Chen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0303073 |
| URL | https://arxiv.org/abs/quant-ph/0303073 |
| DOI | 10.1140/epjd/e2003-00043-7 |
| Journal | Eur.Phys.J.D23:305-313,2003 |
Abstract
By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic physics, quantum optics, nuclear physics and laser physics are obtained. It is shown that the {\it explicit} solutions may also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator ({\it i. e.}, the {\it time-independent} invariant) for some quantum systems without quasi-algebraic structures. The global and topological properties of geometric phases and their adiabatic limit in time-dependent quantum systems/models are briefly discussed.
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"abstract": "By using the Lewis-Riesenfeld theory and the invariant-related unitary\ntransformation formulation, the exact solutions of the {\\it time-dependent}\nSchr\\\"{o}dinger equations which govern the various Lie-algebraic quantum\nsystems in atomic physics, quantum optics, nuclear physics and laser physics\nare obtained. It is shown that the {\\it explicit} solutions may also be\nobtained by working in a sub-Hilbert-space corresponding to a particular\neigenvalue of the conserved generator ({\\it i. e.}, the {\\it time-independent}\ninvariant) for some quantum systems without quasi-algebraic structures. The\nglobal and topological properties of geometric phases and their adiabatic limit\nin time-dependent quantum systems/models are briefly discussed.",
"arxiv_id": "quant-ph/0303073",
"authors": [
"Jian Qi Shen",
"Hong Yi Zhu",
"Pan Chen"
],
"categories": [
"quant-ph"
],
"doi": "10.1140/epjd/e2003-00043-7",
"journal_ref": "Eur.Phys.J.D23:305-313,2003",
"title": "A unified approach to exact solutions of time-dependent Lie-algebraic quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0303073"
},
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