New quasi-exactly solvable class of generalized isotonic oscillators

Abstract

We introduce a new family of quasi-exactly solvable generalized isotonic oscillators which are based on the pseudo-Hermite exceptional orthogonal polynomials. We obtain exact closed-form expressions for the energies and wavefunctions as well as the allowed potential parameters for the first two members of the family using the Bethe ansatz method. Numerical calculations of the energies reveal that member potentials have multiple quasi-exactly solvable eigenstates and the number of states for higher members are parameter dependent.

14 pages; 4 figures

References in corpus (3)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• The generalized quantum isotonic oscillator
• Generalized quantum isotonic nonlinear oscillator in d dimensions

Cited by in corpus (5)

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• Bethe ansatz solutions and hidden $sl(2)$ algebraic structure for a class of quasi-exactly solvable systems
• Perturbation-based Non-perturbative Method
• Quasi-exactly solvable Schrödinger equations, symmetric polynomials, and functional Bethe ansatz method