More on an exactly solvable position-dependent mass Schroedinger equation in two dimensions: Algebraic approach and extensions to three dimensions
摘要
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. Finally, the two-dimensional model is extended to two integrable and exactly solvable (but not superintegrable) models in three dimensions, depicting a particle in a semi-infinite parallelepipedal or cylindrical channel, respectively.
引用
@article{arxiv.quant-ph/0612094,
title = {More on an exactly solvable position-dependent mass Schroedinger equation in two dimensions: Algebraic approach and extensions to three dimensions},
author = {C. Quesne},
journal= {arXiv preprint arXiv:quant-ph/0612094},
year = {2007}
}
备注
23 pages, no figure