Additional restrictions on quasi-exactly solvable systems
arXiv:math-ph/0604061 · doi:10.1007/s11232-007-0015-2
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.
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