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arXiv · 1607.02929

Quasi-exactly solvable symmetrized quartic and sextic polynomial oscillators

C. Quesne
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Abstract

The symmetrized quartic polynomial oscillator is shown to admit an sl(2,$\R$) algebraization. Some simple quasi-exactly solvable (QES) solutions are exhibited. A new symmetrized sextic polynomial oscillator is introduced and proved to be QES by explicitly deriving some exact, closed-form solutions by resorting to the functional Bethe ansatz method. Such polynomial oscillators include two categories of QES potentials: the first one containing the well-known analytic sextic potentials as a subset, and the second one of novel potentials with no counterpart in such a class.

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BibTeXRIS

C. Quesne. 2016-07-11. Quasi-exactly solvable symmetrized quartic and sextic polynomial oscillators. https://doi.org/10.1140/epjp%2Fi2017-11718-y

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