Spectral structure and solution of fractional hydrogen atom difference equations

Abstract

In this study, discrete fractional hydrogen atom (DFHA) operators are presented. Hydrogen atom differential equations have series solution due to having singularity and also obtaining a series solution for DFHA equations have some difficulties, for this reason, we study to obtain solution of DFHA equations by means of nabla Laplace transform. In addition to all these, we show self-adjointness of the DFHA operator and some spectral properties, like orthogonality of distinct eigenfunctions, reality of eigenvalues. Finally, we find an analytical solution of the problem under different q(t) potential functions, different fractional orders and different eigenvalues and the results obtained are illustrated by tables and simulations.