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

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 Hamilton...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-05, Vol.48 (21), p.215204-17
Main Authors: Kikodio, P Kayupe, Mouayn, Z
Format: Article
Language:English
Subjects:
Coherence
coherent states
Exact solutions
Laguerre polynomials
Mathematical analysis
Oscillators
Polynomials
Pöschl-Teller potential
Representations
Symmetry
Wave functions
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Summary: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 , 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 . We also discuss their associated coherent states transform which leads to an integral representation of Hankel type for Laguerre functions.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/21/215204