dorsal/arxiv
View SchemaTime-dependent Schr\"odinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states
| Authors | Michael Martin Nieto, D. Rodney Truax |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9811076 |
| URL | https://arxiv.org/abs/quant-ph/9811076 |
| DOI | 10.1063/1.533269 |
| Journal | J.Math.Phys. 41 (2000) 2753-2767 |
Abstract
Using the transformations from paper I, we show that the Schr\"odinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is deomonstrated.
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"abstract": "Using the transformations from paper I, we show that the Schr\\\"odinger\nequations for: (1)systems described by quadratic Hamiltonians, (2) systems with\ntime-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie\nspace-time symmetry algebras. The generators of the symmetry algebras are\nobtained explicitly for each case and sets of number-operator states are\nconstructed. The algebras and the states are used to compute\ndisplacement-operator coherent and squeezed states. Some properties of the\ncoherent and squeezed states are calculated. The classical motion of these\nstates is deomonstrated.",
"arxiv_id": "quant-ph/9811076",
"authors": [
"Michael Martin Nieto",
"D. Rodney Truax"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.533269",
"journal_ref": "J.Math.Phys. 41 (2000) 2753-2767",
"title": "Time-dependent Schr\\\"odinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states",
"url": "https://arxiv.org/abs/quant-ph/9811076"
},
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