Analytical solutions of the three-dimensional Schr?dinger equation with an exponentially changing effective mass

Abstract

For an effective mass distribution that is an exponential function of the radial coordinate, the analytical solutions of the three-dimensional Schrdinger equ ation are obtained by using the coordinate transformation method for the referen ce problems with Coulomb potential, Kratzer potential and spherically square pot ential well of infinite depth, respectively. The explicit analytical expressions for the energy eigenvalues and the corresponding eigenfunctions of the three sy stems are presented.