Additional restrictions on quasi-exactly solvable systems

Details Additional restrictions on quasi-exactly solvable systems Additional restrictions on quasi-exactly solvable systems

2006-04-25

arxiv.org/abs/math-ph/0604061v1

Physics

Mathematical Physics

11 pages, 3 figures, extended version of talk given at the International Workshop on Classical and Quantum Integrable Systems

Scientific paper

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.

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