Squeezed States and Hermite polynomials in a Complex Variable
Quantum Physics
2015-06-17 v1 Mathematical Physics
math.MP
Abstract
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].
Cite
@article{arxiv.1308.4730,
title = {Squeezed States and Hermite polynomials in a Complex Variable},
author = {S. T. Ali and K. Gorska and A. Horzela and F. H. Szafraniec},
journal= {arXiv preprint arXiv:1308.4730},
year = {2015}
}
Comments
15 pages