Quasi-exactly solvable symmetrized quartic and sextic polynomial oscillators
Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050, Brussels, Belgium
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Accepted: 13 September 2017
Published online: 2 November 2017
The symmetrized quartic polynomial oscillator is shown to admit an 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2017