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arXiv · 1308.4730

Squeezed States and Hermite polynomials in a Complex Variable

S. T. Ali·K. Gorska·A. Horzela·F. H. Szafraniec
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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)].

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S. T. Ali, K. Gorska, A. Horzela, F. H. Szafraniec. 2013-08-21. Squeezed States and Hermite polynomials in a Complex Variable. https://doi.org/10.1063/1.4861932

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