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Additional constraints on quasi-exactly solvable systems

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Abstract

We consider constraints on two-dimensional quantum mechanical systems in domains with boundaries. The constraints result from the Hermiticity requirement for the corresponding Hamiltonians. We construct new two-dimensional families of formally exactly solvable systems. Taking the mentioned constraints into account, we show that the systems are in fact 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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  1. Institute for High Energy Physics, Protvino, Moscow Oblast, Russia

    S. M. Klishevich

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 237–248, February, 2007.

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Klishevich, S.M. Additional constraints on quasi-exactly solvable systems. Theor Math Phys 150, 203–212 (2007). https://doi.org/10.1007/s11232-007-0015-2

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