COHERENT STATES ON THE CIRCLE

Citation
Ja. Gonzalez et Ma. Delolmo, COHERENT STATES ON THE CIRCLE, Journal of physics. A, mathematical and general (Print), 31(44), 1998, pp. 8841-8857
Citations number
24
Categorie Soggetti
Physics,"Physycs, Mathematical
ISSN journal
03054470
Volume
31
Issue
44
Year of publication
1998
Pages
8841 - 8857
Database
ISI
SICI code
0305-4470(1998)31:44<8841:>2.0.ZU;2-I
Abstract
A careful study of the physical properties of a family of coherent sta tes an the circle, introduced some years ago by de Bievre and Gonzalez (in 1992 Semiclassical behaviour of the Weyl correspondence on the ci rcle Group Theoretical Methods in Physics vol I (Madrid: Ciemat)), is carried out. They were obtained from the Weyl-Heisenberg coherent stat es in L-2(R) by means of the Weil-Brezin-Zak transformation, they are labelled by the points of the cylinder S-1 x R, and they provide a rea lization of L-2(S-1) by entire functions(similar to the well known Foc k-Bargmann construction). In particular, we compute the expectation va lues of the position and momentum operators on the circle and we discu ss the Heisenberg uncertainty relation.