Analytical solution to position dependent mass Schrodinger equation

Using a recently developed technique to solve the Schrodinger equation for constant mass, we have studied the regime in which the mass varies with position, i.e. the position-dependent mass Schrodinger equation (PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential V(x). We have also studied the structural analogy between the PDMSE and the two-level atomic system interacting with a classical field.