A Note Basis Properties for Fractional Hydrogen Atom Equation

TL;DR

This paper conducts spectral analysis of a fractional Sturm-Liouville problem with singularity at zero, exploring eigenproperties and fundamental theorems relevant to the fractional hydrogen atom equation.

Contribution

It provides new insights into the eigenvalues and eigenfunctions of fractional Sturm-Liouville problems with singularities, specifically for the fractional hydrogen atom equation.

Findings

Eigenvalues are real and eigenfunctions are orthogonal.

Established fundamental properties of eigenfunctions and eigenvalues.

Presented key theorems and lemmas for the fractional hydrogen atom equation.

Abstract

In this paper, spectral analysis of fractional Sturm Liouville problem defined on (0,1], having the singularity of type at zero and research the fundamental properties of the eigenfunctions and eigenvalues for the operator. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively. Furthermore,we give some important theorems and lemmas for fractional hydrogen atom equation.