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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00553612" target="_blank" >RIV/61389005:_____/22:00553612 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1088/1751-8121/ac43cc" target="_blank" >https://doi.org/10.1088/1751-8121/ac43cc</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/ac43cc" target="_blank" >10.1088/1751-8121/ac43cc</a>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/EF18_053%2F0017163" target="_blank" >EF18_053/0017163: Physicists on the move II</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Volume of the periodical

55

Issue of the periodical within the volume

4

Country of publishing house

GB - UNITED KINGDOM

Number of pages

31

Pages from-to

045205

UT code for WoS article

000744267400001

EID of the result in the Scopus database

2-s2.0-85124146373