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Journal of Physics A Mathematical and General

The quantum Schrodinger equation and the q-deformation of the hydrogen atom

Zing-Chang Song, Liao Li

Published Feb 7, 1992• 25 citations
Publisher

Abstract

By employing the non-commutative differential calculus on the quantum orthogonal planes, the authors investigate the deformed version of the Schrodinger equation for the attractive Coulomb potential V(r)=-e 2 /r. The solutions show the quantum group symmetry, and the calculated energy eigenvalues seem to be proportional to (n) -2 which is in agreement with the energy levels of the hydrogen atom in the limit of q to 1.

DOI
10.1088/0305-4470/25/3/019

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The Hypergeometric method was used to describe radial equations by probeneus approaximation at a singular regular point. Schrodinger equations radial part was reduced into differential equations with variable substitution. By using q-deformed momentum parameter and Coulomb potential as well as variable substitution, the second order of Schrodinger equation with centrifugal approach for q-deformed momentum in Coulomb potential can be solved with Hypergeometric method. The analytical result of energy spectrum and wave function with quantum number and q-deformed variations, while the numerical result for energy spectrum can be calculated by using Matlab 2013 software.