Quantum mechanics without potential function

DOI10.1063/1.4927262zbMath1330.81105arXiv1408.4003OpenAlexW3100977967MaRDI QIDQ5500747

A. D. Alhaidari, Mourad E. H. Ismail

Publication date: 10 August 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.4003

zbMATH Keywords

orthogonal polynomialsquantum mechanicspotential function

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) (2)-body potential quantum scattering theory (81U05) Other special orthogonal polynomials and functions (33C47) Alternative quantum mechanics (including hidden variables, etc.) (81Q65)

Related Items (20)

Progressive approximation of bound states by finite series of square-integrable functions ⋮ 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 ⋮ Solution of the nonrelativistic wave equation using the tridiagonal representation approach ⋮ Series solution of a ten-parameter second-order differential equation with three regular singularities and one irregular singularity ⋮ Quantum systems associated with the Hahn and continuous Hahn polynomials ⋮ Open problem in orthogonal polynomials ⋮ Energy spectrum design and potential function engineering ⋮ Wilson-Racah quantum system ⋮ Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on Orthogonal Polynomials ⋮ Exact scattering and bound states solutions for novel hyperbolic potentials with inverse square singularity ⋮ Bound states and the potential parameter spectrum ⋮ Bound states of an inverse-cube singular potential: A candidate for electron-quadrupole binding ⋮ Four-parameter \(1/r^2\) singular short-range potential with rich bound states and a resonance spectrum ⋮ Exponentially confining potential well ⋮ Solutions of a Bessel-type differential equation using the tridiagonal representation approach ⋮ 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 ⋮ Orthogonal polynomials derived from the tridiagonal representation approach

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