$\hbar$-expansion for the Schr\"odinger equation with a   position-dependent mass
  A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger 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. 
D. A. Kulikov, V. M. Shapoval
quant-ph