dorsal/arxiv
View SchemaThe Schr\"odinger system H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx} +\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2
| Authors | Michael Martin Nieto, D. Rodney Truax |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911094 |
| URL | https://arxiv.org/abs/quant-ph/9911094 |
| DOI | 10.1006/aphy.2001.6144 |
| Journal | Ann. Phys. 292 (2001) 1 |
Abstract
In this paper, we attack the specific time-dependent Hamiltonian problem H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx} +\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2. This corresponds to a time-dependent mass (TM) Schr\"odinger equation. We give the specific transformations to i) the more general quadratic (TQ) Schr\"odinger equation and to ii) a different time-dependent oscillator (TO) equation. For each Schr\"odinger system, we give the Lie algebra of space-time symmetries, the number states, the coherent states, the squeezed-states and the time-dependent <x>, <p>, (\Delta x)^2, (\Delta p)^2, and uncertainty product.
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"abstract": "In this paper, we attack the specific time-dependent Hamiltonian problem\nH=-{1/2}e^{\\Upsilon(t-t_o)}\\partial_{xx}\n+\\lfrac{1}{2}\\omega^2e^{-\\Upsilon(t-t_o)}x^2. This corresponds to a\ntime-dependent mass (TM) Schr\\\"odinger equation. We give the specific\ntransformations to i) the more general quadratic (TQ) Schr\\\"odinger equation\nand to ii) a different time-dependent oscillator (TO) equation. For each\nSchr\\\"odinger system, we give the Lie algebra of space-time symmetries, the\nnumber states, the coherent states, the squeezed-states and the time-dependent\n\u003cx\u003e, \u003cp\u003e, (\\Delta x)^2, (\\Delta p)^2, and uncertainty product.",
"arxiv_id": "quant-ph/9911094",
"authors": [
"Michael Martin Nieto",
"D. Rodney Truax"
],
"categories": [
"quant-ph"
],
"doi": "10.1006/aphy.2001.6144",
"journal_ref": "Ann. Phys. 292 (2001) 1",
"title": "The Schr\\\"odinger system H=-{1/2}e^{\\Upsilon(t-t_o)}\\partial_{xx} +\\lfrac{1}{2}\\omega^2e^{-\\Upsilon(t-t_o)}x^2",
"url": "https://arxiv.org/abs/quant-ph/9911094"
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