Additional restrictions on quasi-exactly solvable systems
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
In this paper we discuss constraints on two-dimensional quantum-mechanical systems living in domains with boundaries. The constrains result from the requirement of hermicity of corresponding Hamiltonians. We construct new two-dimensional families of formally exactly solvable systems and applying such constraints show that in real the systems are quasi-exactly solvable at best. Nevertheless in the context of pseudo-Hermitian Hamiltonians some of the constructed families are exactly solvable.
Keywords
Cite
@article{arxiv.math-ph/0604061,
title = {Additional restrictions on quasi-exactly solvable systems},
author = {Sergey Klishevich},
journal= {arXiv preprint arXiv:math-ph/0604061},
year = {2015}
}
Comments
11 pages, 3 figures, extended version of talk given at the International Workshop on Classical and Quantum Integrable Systems "CQIS-06", Protvino, Russia, January 23-26, 2006