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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149160 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| id |
nasplib_isofts_kiev_ua-123456789-149160 |
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Quesne, C. 2019-02-19T17:51:13Z 2019-02-19T17:51:13Z 2009 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 https://nasplib.isofts.kiev.ua/handle/123456789/149160 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations |
| spellingShingle |
Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations Quesne, C. |
| 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 |
| author |
Quesne, C. |
| author_facet |
Quesne, C. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149160 |
| fulltext |
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| 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. |
| work_keys_str_mv |
AT quesnec pointcanonicaltransformationversusdeformedshapeinvarianceforpositiondependentmassschrodingerequations |
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2025-11-24T10:27:30Z |
| last_indexed |
2025-11-24T10:27:30Z |
| _version_ |
1850844690609340416 |