Borzov, V. V. Generalized oscillator and its coherent states. (English. Russian original) Zbl 1146.81029 Theor. Math. Phys. 153, No. 3, 1656-1670 (2007); translation from Teor. Mat. Fiz. 153, No. 3, 363-380 (2007). Summary: We construct a system (a generalized oscillator) that is similar to the oscillator and is related to a system of orthogonal polynomials on the real axis. We define coherent states in the Fock space associated with the generalized oscillator. In the example of the generalized oscillator related to the Gegenbauer polynomials, we prove the (super)completeness of these coherent states, i.e., we construct a measure determining a partition of unity. We present a formula that allows calculating the Mandel parameter for the constructed coherent states. Cited in 2 Documents MSC: 81R30 Coherent states 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81R15 Operator algebra methods applied to problems in quantum theory 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:orthogonal polynomials; harmonic oscillator; generalized oscillator; creation operator; annihilation operator; coherent state; mandel parameter PDFBibTeX XMLCite \textit{V. V. Borzov}, Theor. Math. Phys. 153, No. 3, 1656--1670 (2007; Zbl 1146.81029); translation from Teor. Mat. Fiz. 153, No. 3, 363--380 (2007) Full Text: DOI References: [1] G. Szegö, Orthogonal Polynomials (Amer. Math. Soc. Colloq. Publ., Vol. 23), Amer. Math. Soc., Providence, R. I. (1959). [2] S. Yu. Slavyanov and W. 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