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arXiv:quant-ph/0307133

Coherent states and Chebyshev polynomials

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

Published Jul 18, 2003• 10 citations
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Abstract

We define the coherent states for the oscillator-like systems, connected with the Chebyshev polynomials $T_n(x)$ and $U_n(x)$ of the 1-st and 2-nd kind.

DOI
10.48550/arxiv.quant-ph/0307133

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We define the coherent states for the oscillator-like systems, connected with the Chebyshev polynomials Tn(x)T_n(x)Tn​(x) and Un(x)U_n(x)Un​(x) of the 1-st and 2-nd kind.
In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained for another variant of Krawtchouk oscillator in the paper [N.M.Atakishiev and S.K.Suslov, Difference analogs of the harmonic oscillator, Teor. Mat. Fiz., 85, 64-73 (1990)] from other point of view. Our definition of coherent states is close to one given in [B.Roy and P.Roy, Phase properties of a new nonlinear coherent state, quant-ph/0002043] This investigation is partially supported by RFBR grant No 06-01-00451