Coherent states on the circle

Abstract

A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bièvre and González in [DG 92], is carried out. They were obtained from the Weyl-Heisenberg coherent states in $L^2(\mathbb{R})$ by means of the Weil-Brezin-Zak transformation, they are labeled by the points of the cylinder $S^1\times \mathbb{R}$, 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.

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

References in corpus (1)

• Coherent states for a quantum particle on a circle

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