Squeezed states and Hermite polynomials in a complex variable

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4861932· OSTI ID:22251120

Ali, S. Twareque, E-mail: [e-mail] ^[1]; Górska, K., E-mail: [e-mail]; Horzela, A., E-mail: [e-mail] ^[2]; Szafraniec, F. H., E-mail: [e-mail] ^[3]

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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)

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)].

• OSTI ID: 22251120
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTIC FUNCTIONS
ANNIHILATION OPERATORS
EIGENSTATES
EXCITED STATES
FLAVOR MODEL
HERMITE POLYNOMIALS