Analytic study of conformable Schrodinger equation with Hydrogen atom

TL;DR

This paper explores the conformable Schrödinger equation for hydrogen atoms, deriving wave functions and energy levels, and analyzing how probability densities change with the conformability parameter.

Contribution

It introduces solutions to the conformable Schrödinger equation for hydrogen, extending traditional quantum mechanics to include conformable derivatives.

Findings

Probability density transitions smoothly from α=0.5 to α=1

Energy levels reduce to traditional values at α=1

Wave functions are explicitly derived for conformable potential

Abstract

In this paper, the conformable Schrodinger equation for hydrogen atom with given conformable potential is solved. The conformable wave functions and energy levels are obtained, and the traditional energy levels and wave function for hydrogen atom are recovered when $\alpha = 1$. The probability density for the first three levels and different values of $\alpha$ is plotted. It is observed that the probability density gradually convert from $\alpha=0.5$ to $\alpha = 1$ for all levels.