Hamiltonians with position-dependent mass, deformations and supersymmetry

Abstract

A new method for generating exactly solvable Schrödinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schrödinger equations, which can be dealt with by using a supersymmetric quantum mechanical approach combined with a deformed shape-invariance condition. The solvability of the latter is shown to impose the form of both the deformed superpotential and the position-dependent mass. The conditions for the existence of bound states are determined. A lot of examples are provided and the corresponding bound-state spectrum and wavefunctions are reviewed.

11 pages, no figure, presented at IV International Symposium Quantum Theory and Symmetries, Varna, Bulgaria, 15-21 August 2005