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Difference analogs of the harmonic oscillator. (English. Russian original) Zbl 1189.81099
Theor. Math. Phys. 85, No. 1, 1055-1062 (1990); translation from Teor. Mat. Fiz. 85, No. 1, 64-73 (1990).
From the text: The wave functions of the harmonic oscillator are often used as a basis to describe the properties of various quantum-mechanical systems. It is also of interest to construct difference analogs of these wave functions, which could be used to study physical systems on lattices. In this paper, we therefore consider two models of a difference oscillator; their wave functions admit representation in terms of Kravchuk (Krawtchouk) polynomials and Hermite \(q\)-polynomials, respectively. Factorization of the difference Hamiltonian makes it possible to determine the generators of the dynamical symmetry group for both models. The connections with representations of the classical and quantum \(\text{SU}(2)\) groups are discussed.

MSC:
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
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