Three-dimensional effective mass Schrodinger equation: harmonic and Morse-type potential solutions
In this work, a scheme to generate exact wave functions and eigenvalues for the spherically symmetric three-dimensional position-dependent effective mass Schrodinger equation is presented. The methodology is implemented by means of separation of variables and point canonical transformations that allow to recognize a radial dependent equation with important differences as compared with the one-dimensional position dependent mass problem, which has been widely studied. This situation deserves to consider the boundary conditions of the emergent problem. To obtain specific exact solutions, the methodology requires known solutions of ordinary one-dimensional Schrodinger equations. We have preferred those applications that use the harmonic oscillator and the Morse oscillator solutions.
position-dependent effective mass harmonic potential morse potential three dimensional schrodinger equation