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A new class of coherent states with Meixner–Pollaczek polynomials for the Gol’dman–Krivchenkov Hamiltonian

Zouhaı̈r Mouayn

A class of generalized coherent states with a new type of the identity resolution is constructed by replacing the labeling parameter of the canonical coherent states by Meixner–Pollaczek polynomials with specific parameters. The constructed coherent states belong to the state Hilbert space of the Gol'dman–Krivchenkov Hamiltonian.

arXiv:1004.3589Journal of Physics A Mathematical and TheoreticalJun 17, 20107 citations

A new class of coherent states with Meixne–Pollaczek polynomials for the Gol'dman–Krivchenkov Hamiltonian

Zouhaı̈r Mouayn

Journal of Physics A Mathematical and TheoreticalJul 12, 20100 citations

The generalized coherent states for oscillators, Connected with Meixner and Meixner-Pollaczek polynomials % %

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

The investigation of the generalized coherent states for oscillator-like systems connected with given family of orthogonal polynomials is continued. In this work we consider oscillators connected with Meixner and Meixner-Pollaczek polynomials and define generalized coherent states for these oscillators. The completeness condition for these states is proved by the solution of the related classical moment problem. The results are compared with the other authors ones. In particular, we show that the Hamiltonian of the relativistic model of linear harmonic oscillator can be thought of as the linearization of the quadratic Hamiltonian which naturally arised in our formalism.The investigation of the generalized coherent states for oscillator-like systems connected with given family of orthogonal polynomials is continued. In this work we consider oscillators connected with Meixner and Meixner-Pollaczek polynomials and define generalized coherent states for these oscillators. The completeness condition for these states is proved by the solution of the related classical moment problem. The results are compared with the other authors ones. In particular, we show that the Hamiltonian of the relativistic model of linear harmonic oscillator can be thought of as the linearization of the quadratic Hamiltonian which naturally arised in our formalism.

arXiv:quant-ph/0503091Mar 9, 20050 citations

New coherent states with Laguerre polynomials coefficients for the symmetric Pöschl–Teller oscillator

P Kayupe Kikodio, Zouhaı̈r Mouayn

We construct new coherent states labeled by points z of the complex plane and depending on three parameters and by replacing the coefficients of the canonical coherent states by Laguerre polynomials with an order depending on γ . These coherent states are superpositions of eigenstates of the Hamiltonian with a symmetric Pöschl–Teller potential indexed by ν , which solve an -identity operator while the resolution of the identity of the states Hilbert space is acheived at the limit We obtain their wave functions in a closed form for a special case of parameters γ and ν . We also discuss their associated coherent states transform which leads to an integral representation of Hankel type for Laguerre functions.We construct new coherent states labeled by points z of the complex plane and depending on three parameters and by replacing the coefficients of the canonical coherent states by Laguerre polynomials with an order depending on γ . These coherent states are superpositions of eigenstates of the Hamiltonian with a symmetric Pöschl–Teller potential indexed by ν , which solve an -identity operator while the resolution of the identity of the states Hilbert space is acheived at the limit We obtain their wave functions in a closed form for a special case of parameters γ and ν . We also discuss their associated coherent states transform which leads to an integral representation of Hankel type for Laguerre functions.

arXiv:1501.00895Journal of Physics A Mathematical and TheoreticalMay 6, 20151 citation

COHERENT STATES WITH COMPLEX FUNCTIONS

Kengatharam Thirulogasanthar, G. Honnouvo

Abstract. The canonical coherent states are expressed as infinite series in powers of a complex number z in their infinite series version. In this article we present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states. 1.Abstract. The canonical coherent states are expressed as infinite series in powers of a complex number z in their infinite series version. In this article we present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states. 1.

Jan 1, 20031 citation

Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

Journal of Mathematical SciencesJun 1, 20065 citations

A NEW CLASS OF COHERENT STATES WITH MEIXNER-POLLACZEK POLYNOMIALS FOR THE GOL’DMAN-KRIVCHENKOV HAMILTONIAN

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