Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schr\"odinger Equation in Two Dimensions
Abstract
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schr\"odinger equations.
Keywords
Cite
@article{arxiv.0705.2577,
title = {Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schr\"odinger Equation in Two Dimensions},
author = {Christiane Quesne},
journal= {arXiv preprint arXiv:0705.2577},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/