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Title: Squeezed states and Hermite polynomials in a complex variable

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. Pure Appl. Math. 14, 187 (1961)].
Authors:
 [1] ; ;  [2] ;  [3]
  1. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8 (Canada)
  2. H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Division of Theoretical Physics, ul. Eliasza-Radzikowskiego 152, PL 31-342 Kraków (Poland)
  3. Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, PL 30-348 Kraków (Poland)
Publication Date:
OSTI Identifier:
22251120
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANALYTIC FUNCTIONS; ANNIHILATION OPERATORS; EIGENSTATES; EXCITED STATES; FLAVOR MODEL; HERMITE POLYNOMIALS