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

Journal Article · Wed Mar 15 00:00:00 EDT 2017 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2017.01.023· OSTI ID:22617483

Schulze-Halberg, Axel ^[1]; Roy, Pinaki ^[2]

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1. Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States)
2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)

We construct energy-dependent potentials for which the Schrödinger equations admit solutions 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.

• OSTI ID: 22617483
• Journal Information: Annals of Physics, Vol. 378; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
LAGUERRE POLYNOMIALS
MATHEMATICAL SOLUTIONS
SCHROEDINGER EQUATION