On Schrödinger equation with potential U = - αr^-1 + βr + kr² and the bi-confluent Heun functions theory

2011/10/24 by E. Ovsiyuk, Ovsiyuk, E., M. Amirfachrian +4
Mathematics · Physics and Astronomy · #35 #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics #acm:35 #math-ph #math.MP #msc:35

paper · pdf · doi:10.48550/arxiv.1110.5121

8 pages, 1 figure, Report to 18 Conference NPCS-2011, May 17-20, 2011, Minsk, Belarus

arxiv created 2011/10/24 · openalex publication_date 2011/10/24 · arxiv updated 2011/10/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is shown that Schrödinger equation with combination of three potentials U = - α r^-1 + β r + kr², Coulomb, linear and harmonic, the potential often used to describe quarkonium, is reduced to a bi-confluent Heun differential equation. The method to construct its solutions in the form of polynomials is developed, however with additional constraints in four parameters of the model, α, β, k, l. The energy spectrum looks as a modified combination of oscillator and Coulomb parts.

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