$\hslash$-expansion for the Schrödinger equation with a position-dependent mass

Abstract

A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schrödinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy eigenvalues for the Coulomb potential in the presence of position-dependent mass and we derive the inequalities regulating the shifts of the energy levels from their constant-mass positions.

10 pages, translated version of a paper: D.A. Kulikov, V.M. Shapoval, J.Phys.Stud. 15 (2011) 4001