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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF18_053%2F0017163" target="_blank" >EF18_053/0017163: Fyzici v pohybu II</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

55

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

31

Strana od-do

045205

Kód UT WoS článku

000744267400001

EID výsledku v databázi Scopus

2-s2.0-85124146373