Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters

DOI10.1088/1572-9494/ab5d00zbMath1452.81094arXiv1709.07652OpenAlexW3103106210MaRDI QIDQ3387544

A. D. Alhaidari

Publication date: 13 January 2021

Published in: Communications in Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.07652

zbMATH Keywords

asymptoticsorthogonal polynomialsenergy spectrumphase shifttridiagonal representationrecursion relation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (8)

Progressive approximation of bound states by finite series of square-integrable functions ⋮ Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions ⋮ Energy spectrum design and potential function engineering ⋮ Exponentially confining potential well ⋮ Solutions of a Bessel-type differential equation using the tridiagonal representation approach ⋮ Potential function of the Wilson-Racah quantum system ⋮ Solving Schrödinger equation by mapping it into a Heun-type equation with known solutions ⋮ Confined systems with a linear energy spectrum

Cites Work

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• Bound states of a charged particle in the field of an electric quadrupole in two dimensions
• Asymptotics for the \({}_ 4F_ 3\) polynomials
• Quantum systems associated with the Hahn and continuous Hahn polynomials
• Open problem in orthogonal polynomials
• Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential
• The scattering amplitude for rationally extended shape invariant Eckart potentials
• Wilson-Racah quantum system
• Orthogonal polynomials derived from the tridiagonal representation approach
• Lie algebras for systems with mixed spectra. I. The scattering Pöschl–Teller potential
• SO(2,1) Lie algebra, the Jacobi matrix and the scattering states of the Morse oscillator
• Scattering Theory and Polynomials Orthogonal on the Real Line
• A Relation between the Coefficients in the Recurrence Formula and the Spectral Function for Orthogonal Polynomials
• Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on Orthogonal Polynomials
• Scattering and bound states for a class of non-central potentials
• Orthogonal polynomials from the viewpoint of scattering theory
• Quasi-exactly solvable systems and orthogonal polynomials
• Solution of the nonrelativistic wave equation using the tridiagonal representation approach
• Charged particle in the field of an electric quadrupole in two dimensions
• Quantum mechanics without potential function

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