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arXiv · 2401.04586

Quasi-exactly solvable potentials in Wigner-Dunkl quantum mechanics

C. Quesne
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Abstract

It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the latter can also be rewritten in a simpler way in terms of an extended Dunkl derivative. Furthermore, the Dunkl isotropic oscillator and Dunkl Coulomb potentials in the plane are generalized to quasi-exactly solvable ones. In the former case, potentials with $n+1$ known eigenstates are obtained, whereas, in the latter, sets of $n+1$ potentials associated with a given energy are derived.

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C. Quesne. 2024-01-09. Quasi-exactly solvable potentials in Wigner-Dunkl quantum mechanics. https://arxiv.org/abs/2401.04586

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