Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions
An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the mom...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147365 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 52 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147365 |
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Quesne, C. 2019-02-14T14:44:57Z 2019-02-14T14:44:57Z 2007 Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 52 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R12; 81R15 https://nasplib.isofts.kiev.ua/handle/123456789/147365 An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schrödinger equations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions |
| spellingShingle |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions Quesne, C. |
| title_short |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions |
| title_full |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions |
| title_fullStr |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions |
| title_full_unstemmed |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions |
| title_sort |
quadratic algebra approach to an exactly solvable position-dependent mass schrödinger equation in two dimensions |
| author |
Quesne, C. |
| author_facet |
Quesne, C. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schrödinger equations.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147365 |
| citation_txt |
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 52 назв. — англ. |
| work_keys_str_mv |
AT quesnec quadraticalgebraapproachtoanexactlysolvablepositiondependentmassschrodingerequationintwodimensions |
| first_indexed |
2025-12-07T20:23:04Z |
| last_indexed |
2025-12-07T20:23:04Z |
| _version_ |
1850882375672659968 |