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Families of quasi-exactly solvable extensions of the quantum oscillator in curved spaces

par Quesne, Christiane
Référence Journal of mathematical physics, 58, 5, 052104
Publication Publié, 2017-05

Article révisé par les pairs

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Résumé :

We introduce two new families of quasi-exactly solvable (QES) extensions of the oscillator in a d-dimensional constant-curvature space. For the first three members of each family, we obtain closed-form expressions of the energies and wavefunctions for some allowed values of the potential parameters using the Bethe ansatz method. We prove that the first member of each family has a hidden sl(2, ℝ) symmetry and is connected with a QES equation of the first or second type, respectively. One-dimensional results are also derived from the d-dimensional ones with d ≥ 2, thereby getting QES extensions of the Mathews-Lakshmanan nonlinear oscillator.