Position-dependent mass Schrodinger equation for the q-deformed Woods-Saxson plus hyperbolic tangent potential

Abstract

In this work, we propose a new potential called the "q-deformed Woods-Saxon plus hyperbolic tangent potential." We derive the generalized Schrödinger equation for quantum mechanical systems with position-dependent masses under these potentials using the Nikiforov-Uvarov method, with the mass relationship defined as m(x)=m_1⁄((1+qe^(-2λx))). The solutions to this equation, expressed in terms of hypergeometric functions and Jacobi polynomials, offer insights into the quantum behavior of particles. The energy eigenvalues depend on system parameters such as the deformation parameter q, potential parameters, and quantum numbers. We analyzed the effect of the deformation parameter q numerically and visually using different values of these parameters.