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Coherent states on the circle

Jose A. Gonzalez·Mariano A. del Olmo
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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 $L^2(\R)$ 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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Jose A. Gonzalez, Mariano A. del Olmo. 1998-09-09. Coherent states on the circle. https://doi.org/10.1088/0305-4470%2F31%2F44%2F012

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