On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00564995" target="_blank" >RIV/61389005:_____/22:00564995 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.physd.2022.133529" target="_blank" >https://doi.org/10.1016/j.physd.2022.133529</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physd.2022.133529" target="_blank" >10.1016/j.physd.2022.133529</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

Popis výsledku v původním jazyce

This work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation between third-order shape-invariant Hamiltonians and the -1/x and -2x hierarchies of rational solutions of the fourth Painleve equation. Such a relation unequivocally establishes the discrete spectrum structure, composed as the union of a finite-and infinite-dimensional sequence of equidistant eigenvalues separated by a gap. The two indices of the generalized Hermite polynomials define the dimension of the finite sequence and the gap. Likewise, the complete set of eigensolutions decomposes into two disjoint subsets, whose elements are written as the product of a polynomial times a weight function supported on the real line. These polynomials fulfill a second-order differential equation and are alternatively determined from a three-term recurrence relation, the initial conditions of which are also fixed in terms of generalized Hermite polynomials.

Název v anglickém jazyce

On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

Popis výsledku anglicky

This work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation between third-order shape-invariant Hamiltonians and the -1/x and -2x hierarchies of rational solutions of the fourth Painleve equation. Such a relation unequivocally establishes the discrete spectrum structure, composed as the union of a finite-and infinite-dimensional sequence of equidistant eigenvalues separated by a gap. The two indices of the generalized Hermite polynomials define the dimension of the finite sequence and the gap. Likewise, the complete set of eigensolutions decomposes into two disjoint subsets, whose elements are written as the product of a polynomial times a weight function supported on the real line. These polynomials fulfill a second-order differential equation and are alternatively determined from a three-term recurrence relation, the initial conditions of which are also fixed in terms of generalized Hermite polynomials.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied 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

Physica. D

ISSN

0167-2789

e-ISSN

1872-8022

Svazek periodika

442

Číslo periodika v rámci svazku

DEC

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

10

Strana od-do

133529

Kód UT WoS článku

000880401700008

EID výsledku v databázi Scopus

2-s2.0-85139497398