Solving Schrödinger equation by mapping it into a Heun-type equation with known solutions

DOI10.1063/5.0017215zbMath1454.81056arXiv1906.11162OpenAlexW3117687944MaRDI QIDQ3386489

A. D. Alhaidari

Publication date: 4 January 2021

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

Full work available at URL: https://arxiv.org/abs/1906.11162

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) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) General spectral theory of ordinary differential operators (34L05) Linear ordinary differential equations and systems (34A30) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (1)

An application of Heun functions in the quantum mechanics of a constrained particle

Cites Work

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• Open problem in orthogonal polynomials
• Wilson-Racah quantum system
• Tridiagonalization and the Heun equation
• Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Series solutions of Heun-type equation in terms of orthogonal polynomials

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