A New Perspective via Fractional Calculus for the Radial Schrödinger Equation

Abstract

Differintegral theorems are applied to solve some ordinary differential equations and fractional differential equations. By using these theorems, we obtain different results in the fractional differintegral forms. In this paper, we aim to solve the radial Schrödinger equation under the potential $ V(r)=H/r^{2}-K/r+Lr^{\kappa} $ in $ \kappa=0,-1,-2 $ cases. We also obtain the solutions in the hypergeometric form.