Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schrödinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the S...

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Дата:2009
Автор: Quesne, C.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2009
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/149160
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 44 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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record_format dspace
spelling irk-123456789-1491602019-02-20T01:27:40Z Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations Quesne, C. On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schrödinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the Schrödinger equation is exactly solvable. This approach has provided the bound-state energy spectrum, as well as the ground-state and the first few excited-state wavefunctions. The general wavefunctions have however remained unknown in explicit form because for their determination one would need the solutions of a rather tricky differential-difference equation. Here we show that solving this equation may be avoided by combining the deformed shape invariance technique with the point canonical transformation method in a novel way. It consists in employing our previous knowledge of the PDM problem energy spectrum to construct a constant-mass Schrödinger equation with similar characteristics and in deducing the PDM wavefunctions from the known constant-mass ones. Finally, the equivalence of the wavefunctions coming from both approaches is checked. 2009 Article Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 44 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81Q05; 81Q60 http://dspace.nbuv.gov.ua/handle/123456789/149160 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schrödinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the Schrödinger equation is exactly solvable. This approach has provided the bound-state energy spectrum, as well as the ground-state and the first few excited-state wavefunctions. The general wavefunctions have however remained unknown in explicit form because for their determination one would need the solutions of a rather tricky differential-difference equation. Here we show that solving this equation may be avoided by combining the deformed shape invariance technique with the point canonical transformation method in a novel way. It consists in employing our previous knowledge of the PDM problem energy spectrum to construct a constant-mass Schrödinger equation with similar characteristics and in deducing the PDM wavefunctions from the known constant-mass ones. Finally, the equivalence of the wavefunctions coming from both approaches is checked.
format Article
author Quesne, C.
spellingShingle Quesne, C.
Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Quesne, C.
author_sort Quesne, C.
title Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
title_short Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
title_full Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
title_fullStr Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
title_full_unstemmed Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
title_sort point canonical transformation versus deformed shape invariance for position-dependent mass schrödinger equations
publisher Інститут математики НАН України
publishDate 2009
url http://dspace.nbuv.gov.ua/handle/123456789/149160
citation_txt Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 44 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT quesnec pointcanonicaltransformationversusdeformedshapeinvarianceforpositiondependentmassschrodingerequations
first_indexed 2023-05-20T17:32:28Z
last_indexed 2023-05-20T17:32:28Z
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