Scattering states of position-dependent mass Schr\"odinger equation with non central potential

In this paper, we study the time-independent Schr"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr"odinger equation can be easily solved analytically through separation of variables. The energy eigenvalues and the normalization constant of the radial wave functions are obtained, as well as the scattering phase shifts.