Hamiltonians with position-dependent mass, deformations and supersymmetry
Quantum Physics
2007-05-23 v1
Abstract
A new method for generating exactly solvable Schr\"odinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schr\"odinger 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.
Cite
@article{arxiv.quant-ph/0512046,
title = {Hamiltonians with position-dependent mass, deformations and supersymmetry},
author = {C. Quesne and B. Bagchi and A. Banerjee and V. M. Tkachuk},
journal= {arXiv preprint arXiv:quant-ph/0512046},
year = {2007}
}
Comments
11 pages, no figure, presented at IV International Symposium Quantum Theory and Symmetries, Varna, Bulgaria, 15-21 August 2005