Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on Orthogonal Polynomials

DOI10.1088/0253-6102/68/6/711zbMath1382.81006OpenAlexW2775283422MaRDI QIDQ4607318

A. D. Alhaidari

Publication date: 13 March 2018

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

Full work available at URL: https://doi.org/10.1088/0253-6102/68/6/711

zbMATH Keywords

wavefunctionasymptoticsorthogonal polynomialspotential functionrecursion relationtridiagonal representations

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Special polynomials in general fields (12E10)

Related Items (11)

Solution of an open problem about two families of orthogonal polynomials ⋮ Series solutions of Laguerre- and Jacobi-type differential equations in terms of orthogonal polynomials and physical applications ⋮ Quantum systems associated with the Hahn and continuous Hahn polynomials ⋮ Energy spectrum design and potential function engineering ⋮ Bound states of an inverse-cube singular potential: A candidate for electron-quadrupole binding ⋮ Exact solvability of two new 3D and 1D non-relativistic potentials within the TRA framework ⋮ Exponentially confining potential well ⋮ Potential function of the Wilson-Racah quantum system ⋮ Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters ⋮ Confined systems with a linear energy spectrum ⋮ Quantum mechanics without potential function

Cites Work

• Wilson-Racah quantum system
• Orthogonal polynomials derived from the tridiagonal representation approach
• SO(2,1) Lie algebra, the Jacobi matrix and the scattering states of the Morse oscillator
• Response to “Comment on ‘Bound states and the potential parameter spectrum’” [J. Math. Phys. 62, 064101 (2021)]
• Quantum mechanics without potential function

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