Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation

Abstract

Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.

12 pages

References in corpus (3)

• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass
• Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $\eta$-pseudo-Hermiticity generators