https://doi.org/10.1140/epjp/i2017-11718-y
Regular Article
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
* e-mail: cquesne@ulb.ac.be
Received:
18
August
2017
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
