Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (4): 1411-1426.

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GENERALIZED DISCRETE Q-HERMITE I POLYNOMIALS AND Q-DEFORMED OSCILLATOR

Kamel MEZLINI1, Néji BETTAIBI2   

  1. 1. High Institute of Applied Sciences and Technologies of Mateur, University of Carthage, Tunisia;
    2. Department of Mathematics, College of Science, Qassim University, KSA
  • Received:2016-01-15 Revised:2018-02-08 Online:2018-08-25 Published:2018-08-25

Abstract: In this paper, we present an explicit realization of q-deformed Calogero-Vasiliev algebra whose generators are first-order q-difference operators related to the generalized discrete q-Hermite I polynomials recently introduced in[14]. Furthermore, we construct the wave functions and we determine the q-coherent states.

Key words: basic orthogonal polynomials, quantum algebra, coherent states

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