A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
High Energy Physics - Theory
2008-11-26 v2 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Quantum Physics
Abstract
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lame, associated Lame, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lame potential) obeys the property of self-isospectrality.
Cite
@article{arxiv.0706.1344,
title = {A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials},
author = {M. V. Ioffe and J. Mateos Guilarte and P. A. Valinevich},
journal= {arXiv preprint arXiv:0706.1344},
year = {2008}
}