Geodesic
Generalized oscillator and its coherent states
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 363-380

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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.
Mots-clés : orthogonal polynomials
Keywords: harmonic oscillator, generalized oscillator, creation operator, annihilation operator, coherent state, Mandel parameter. 
@article{TMF_2007_153_3_a3,
     author = {V. V. Borzov},
     title = {Generalized oscillator and its coherent states},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {363--380},
     publisher = {mathdoc},
     volume = {153},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a3/}
}
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V. V. Borzov. Generalized oscillator and its coherent states. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 363-380. http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a3/