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

TL;DR

This paper analytically solves the position-dependent mass Schrödinger equation with a non-central potential, deriving energy levels, wave functions, and scattering phase shifts to advance understanding of quantum systems with variable mass.

Contribution

It provides an analytical solution to the non-central effective potential problem in the position-dependent mass Schrödinger equation, including scattering states.

Findings

Analytical expressions for energy eigenvalues and wave functions.

Explicit calculation of scattering phase shifts.

Method applicable to generalized non-central potentials.

Abstract

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.