dorsal/arxiv
View SchemaThe Uncertainty Way of Generalization of Coherent States
| Authors | D. A. Trifonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9912084 |
| URL | https://arxiv.org/abs/quant-ph/9912084 |
| Journal | In "Geometry, Integrability and Quantization", Eds. I.M. Mladenov and G.L. Naber (Coral Press, Sofia 2000), p. 257- 282 |
Abstract
The three ways of generalization of canonical coherent states are briefly reviewed and compared with the emphasis laid on the (minimum) uncertainty way. The characteristic uncertainty relations, which include the Schroedinger and Robertson inequalities, are extended to the case of several states. It is shown that the standard SU(1,1) and SU(2) coherent states are the unique states which minimize the second order characteristic inequality for the three generators. A set of states which minimize the Schroedinger inequality for the Hermitian components of the su_q(1,1) ladder operator is also constructed. It is noted that the characteristic uncertainty relations can be written in the alternative complementary form.
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"abstract": "The three ways of generalization of canonical coherent states are briefly\nreviewed and compared with the emphasis laid on the (minimum) uncertainty way.\nThe characteristic uncertainty relations, which include the Schroedinger and\nRobertson inequalities, are extended to the case of several states. It is shown\nthat the standard SU(1,1) and SU(2) coherent states are the unique states which\nminimize the second order characteristic inequality for the three generators. A\nset of states which minimize the Schroedinger inequality for the Hermitian\ncomponents of the su_q(1,1) ladder operator is also constructed. It is noted\nthat the characteristic uncertainty relations can be written in the alternative\ncomplementary form.",
"arxiv_id": "quant-ph/9912084",
"authors": [
"D. A. Trifonov"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"journal_ref": "In \"Geometry, Integrability and Quantization\", Eds. I.M. Mladenov\n and G.L. Naber (Coral Press, Sofia 2000), p. 257- 282",
"title": "The Uncertainty Way of Generalization of Coherent States",
"url": "https://arxiv.org/abs/quant-ph/9912084"
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