An iteration algorithm for the time-independent fractional Schrödinger equation with Coulomb potential

Abstract

A numerical formula is derived which gives solutions of the fractional Schrodinger equation in time-independent form in the case of Coulomb potential using Riemann–Liouville definition of the fractional derivative and the quadrature methods. The formula is applied for electron in the nucleus field for multiple values of fractional parameter of the space-dependent fractional Schrodinger equation and for each value of the space-dependent fractional parameter, multiple values of energies are applied. Distances are found at which the probability takes its maximum value. Values of energy obtained in this study corresponding to the maximum value of probability are compared with the energy values resulted from the fractional Bohr’s atom formula in the fractional quantum mechanics.