Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials

0553612 - ÚJF 2023 RIV GB eng J - Článek v odborném periodiku
Hussin, V. - Marquette, I. - Zelaya, Kevin
Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials.
Journal of Physics A-Mathematical and Theoretical. Roč. 55, č. 4 (2022), č. článku 045205. ISSN 1751-8113. E-ISSN 1751-8121
Grant CEP: GA MŠMT EF18_053/0017163
Institucionální podpora: RVO:61389005
Klíčová slova: higher-order shape invariance * fourth Painleve transcendent * orthogonal polynomials * SUSY QM * generalized Okamoto polynomials * exactly solvable quantum models
Obor OECD: Pure mathematics
Impakt faktor: 2.1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1088/1751-8121/ac43cc

We extend and generalize the construction of Sturm-Liouville problems for a family of Hamiltonians constrained to fulfill a third-order shape-invariance condition and focusing on the '-2x/3' hierarchy of solutions to the fourth Painleve transcendent. Such a construction has been previously addressed in the literature for some particular cases but we realize it here in the most general case. The corresponding potential in the Hamiltonian operator is a rationally extended oscillator defined in terms of the conventional Okamoto polynomials, from which we identify three different zero-modes constructed in terms of the generalized Okamoto polynomials. The third-order ladder operators of the system reveal that the complete set of eigenfunctions is decomposed as a union of three disjoint sequences of solutions, generated from a set of three-term recurrence relations. We also identify a link between the eigenfunctions of the Hamiltonian operator and a special family of exceptional Hermite polynomial.
Trvalý link: http://hdl.handle.net/11104/0328368