The Bargmann representation for the quantum mechanics on a sphere. (English) Zbl 1012.81023
Summary: The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced by the authors [J. Phys. A, Math. Gen. 33, 6035-6048 (2000; Zbl 1008.81036)]. The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere \(S^2\).
MSC:
| 81R30 | Coherent states |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
| 81S10 | Geometry and quantization, symplectic methods |
Citations:
Zbl 1008.81036References:
| [1] | Kowalski K., J. Phys. A 33 pp 6035– (2000) · Zbl 1008.81036 · doi:10.1088/0305-4470/33/34/309 |
| [2] | DOI: 10.1063/1.1704034 · Zbl 0127.18701 · doi:10.1063/1.1704034 |
| [3] | DOI: 10.1063/1.1704034 · Zbl 0127.18701 · doi:10.1063/1.1704034 |
| [4] | DOI: 10.1063/1.1704034 · Zbl 0127.18701 · doi:10.1063/1.1704034 |
| [5] | DOI: 10.1016/0370-1573(90)90120-Q · doi:10.1016/0370-1573(90)90120-Q |
| [6] | DOI: 10.1002/cpa.3160140303 · Zbl 0107.09102 · doi:10.1002/cpa.3160140303 |
| [7] | DOI: 10.1006/jfan.1994.1064 · Zbl 0838.22004 · doi:10.1006/jfan.1994.1064 |
| [8] | DOI: 10.1006/jfan.1994.1064 · Zbl 0838.22004 · doi:10.1006/jfan.1994.1064 |
| [9] | Hall B. C., Bull. Am. Math. Soc. 38 pp 43– (2001) · Zbl 0971.22008 · doi:10.1090/S0273-0979-00-00886-7 |
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