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Coherent states for a generalized oscillator in a finite-dimensional Hilbert space. (Russian, English) Zbl 1116.81031

Zap. Nauchn. Semin. POMI 335, 75-99 (2006); translation in J. Math. Sci., New York 143, No. 1, 2738-2753 (2007).
Summary: The construction of oscillator-like systems connected with a given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of systems with finite-dimensional state space. As an example we consider the generalized oscillator connected with Krawtchouk polynomials.

MSC:

81R30 Coherent states
81R12 Groups and algebras in quantum theory and relations with integrable systems
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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