Exactly solvable Schrodinger equations with a position-dependent mass are proposed. Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wavefunctions.
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.
Effective mass Schrödinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrödinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrödinger equation starting from the constant mass Schrödinger equation. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Position-dependent mass, Effective mass Schrödinger equation, Morse potential, Nikiforov-Uvarov method