Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials

The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational extensions of the Rosen-Morse II and Eckart potentials that can be ob...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2012
Автор: Quesne, C.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2012
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/148656
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 48 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Quesne, C.
author_facet Quesne, C.
citation_txt Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 48 назв. — англ.
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container_title Symmetry, Integrability and Geometry: Methods and Applications
description The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational extensions of the Rosen-Morse II and Eckart potentials that can be obtained in first-order supersymmetric quantum mechanics. Such extensions are shown to belong to three different types, the first two strictly isospectral to some starting conventional potential with different parameters and the third with an extra bound state below the spectrum of the latter. In the isospectral cases, the partner of the rational extensions resulting from the deletion of their ground state can be obtained by translating both the potential parameter A (as in the conventional case) and the degree m of the polynomial arising in the denominator. It therefore belongs to the same family of extensions, which turns out to be closed.
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spelling Quesne, C.
2019-02-18T17:36:42Z
2019-02-18T17:36:42Z
2012
Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 48 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81Q05; 81Q60
DOI: http://dx.doi.org/10.3842/SIGMA.2012.080
https://nasplib.isofts.kiev.ua/handle/123456789/148656
The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational extensions of the Rosen-Morse II and Eckart potentials that can be obtained in first-order supersymmetric quantum mechanics. Such extensions are shown to belong to three different types, the first two strictly isospectral to some starting conventional potential with different parameters and the third with an extra bound state below the spectrum of the latter. In the isospectral cases, the partner of the rational extensions resulting from the deletion of their ground state can be obtained by translating both the potential parameter A (as in the conventional case) and the degree m of the polynomial arising in the denominator. It therefore belongs to the same family of extensions, which turns out to be closed.
The author would like to thank Y. Grandati for several useful discussions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
Article
published earlier
spellingShingle Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
Quesne, C.
title Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
title_full Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
title_fullStr Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
title_full_unstemmed Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
title_short Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
title_sort novel enlarged shape invariance property and exactly solvable rational extensions of the rosen-morse ii and eckart potentials
url https://nasplib.isofts.kiev.ua/handle/123456789/148656
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