dorsal/arxiv
View SchemaCoherent states on the circle
| Authors | Jose A. Gonzalez, Mariano A. del Olmo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809020 |
| URL | https://arxiv.org/abs/quant-ph/9809020 |
| DOI | 10.1088/0305-4470/31/44/012 |
| Journal | J.Phys.A31:8841-8857,1998 |
Abstract
A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bi\`evre and Gonz\'alez in [DG 92], is carried out. They were obtained from the Weyl-Heisenberg coherent states in $L^2(\R)$ by means of the Weil-Brezin-Zak transformation, they are labeled by the points of the cylinder $S^1 \times \R$, and they provide a realization of $L^2(S^1)$ by entire functions (similar to the well-known Fock-Bargmann construction). In particular, we compute the expectation values of the position and momentum operators on the circle and we discuss the Heisenberg uncertainty relation.
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"abstract": "A careful study of the physical properties of a family of coherent states on\nthe circle, introduced some years ago by de Bi\\`evre and Gonz\\\u0027alez in [DG 92],\nis carried out. They were obtained from the Weyl-Heisenberg coherent states in\n$L^2(\\R)$ by means of the Weil-Brezin-Zak transformation, they are labeled by\nthe points of the cylinder $S^1 \\times \\R$, and they provide a realization of\n$L^2(S^1)$ by entire functions (similar to the well-known Fock-Bargmann\nconstruction). In particular, we compute the expectation values of the position\nand momentum operators on the circle and we discuss the Heisenberg uncertainty\nrelation.",
"arxiv_id": "quant-ph/9809020",
"authors": [
"Jose A. Gonzalez",
"Mariano A. del Olmo"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/31/44/012",
"journal_ref": "J.Phys.A31:8841-8857,1998",
"title": "Coherent states on the circle",
"url": "https://arxiv.org/abs/quant-ph/9809020"
},
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