Exact solutions of the Schrödinger equation with the position-dependent mass for a hard-core potential

The exact solutions of two-dimensional Schrödinger equation with the position-dependent mass for a hard-core potential are obtained. The eigenvalues related to the position-dependent masses μ1 and μ2, the potential well depth V0 and the effective range r0 can be calculated by the boundary condition. We generalize this quantum system to three-dimensional case. The special cases for l=0,1 are studied in detail. For l=0 and c=0, we find that the energy levels will increase with the parameters μ2, V0 and r0 if μ1>μ2.