Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

Abstract

We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

21 pages,9 figures

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Cited by in corpus (2)

• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• Saturation effect in confined quantum systems with energy-dependent potentials