Coherent states on the circle

Details Coherent states on the circle Coherent states on the circle

1998-09-09

arxiv.org/abs/quant-ph/9809020v1

J.Phys.A31:8841-8857,1998

Physics

Quantum Physics

AMS-TeX file, 20 pages, 4 PostScript figures. To be published in J. Phys. A

Scientific paper

10.1088/0305-4470/31/44/012

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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