Central potential and examples of hidden algebra structure
Y.Brihaye, N.Devaux, P.Kosinski
TL;DR
This paper introduces two generalized Coulomb potentials in quantum mechanics, explores their algebraic eigenfunctions, and discusses related relativistic cases, revealing new algebraic structures in quantum systems.
Contribution
It presents novel generalizations of the Coulomb potential and analyzes their algebraic eigenfunctions, extending understanding of hidden algebraic structures in quantum mechanics.
Findings
Identification of algebraic eigenfunctions for the generalized potentials
Discussion of relativistic counterparts of the potentials
Insights into hidden algebraic structures in quantum systems
Abstract
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems are also discussed.
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