Quasipotential wave functions of a relativistic harmonic oscillator and Pollaczek polynomials

Atakishiev, N. M.

doi:10.1007/bf01017923

Cited by 12 publications

(3 citation statements)

References 4 publications

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“…In [2], in the framework of a two-particle equation of the quasipotential type, the variable ρ was interpreted as the relativistic generalization of a relative coordinate. Quasipotential models of a relativistic oscillator were first considered in [3,4,5]. The ρ-representation or the ρn representation (|n| = 1) may also be used in a so-called generalized Schrödinger (GS) picture in which the analogs of the Schrödinger operators of a particle are independent of both the time and the space coordinates t, x in different representations [6].…”

Section: Introductionmentioning

confidence: 99%

Model of a relativistic oscillator in a generalized Schrödinger picture

Frick

2011

Annalen der Physik

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In a generalized Schrödinger picture, we consider the motion of a relativistic particle in an external field (like in the case of a harmonic oscillator). In this picture the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the Anti de Sitter (AdS) space. We also consider the nonrelativistic limit.

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Section: Introductionmentioning

confidence: 99%

Model of a relativistic oscillator in a generalized Schrödinger picture

Frick

2011

Annalen der Physik

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“…Note that these polynomials occur in the expression of eigenstates of the relativistic linear oscillator [22].…”

Section: Orthogonal Polynomials Attached To Coherent States For the Smentioning

confidence: 99%

Research Article Orthogonal polynomials attached to coherent states for the symmetric Pöschl–Teller oscillator

Ahbli

Patrick

Mouayn

2016

Integral Transforms and Special Functions

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We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients z n / √ n! of the canonical coherent states by a specific generalized factorial x γ n !, γ ≥ 0. These states are superposition of eigenstates of the Hamiltonian with a symmetric Pöschl-Teller potential depending on a parameter ν > 1. The associated Bargmann-type transform is defined for γ = ν. Some results on the infinite square well potential are also derived. For some different values of γ, we discuss two sets of orthogonal polynomials that are naturally attached to these coherent states.

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“…Attempts of such construction ' was undertaken in the work [10] (Meixner and Meixner-Pollaczek polynomials) and in [46] (Hahn polynomials). The Pollaczek polynomials were involved in the description [47] of the wave functions of relativistic model of linear harmonic oscillator in the frame-work of the quasi-potential approach. (For more details on this model and its variants we refer the reader to [48]- [51]).…”

Section: Introductionmentioning

confidence: 99%