A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146528 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum / O. Ragnisco, D. Riglioni // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862694645858828288 |
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| author | Ragnisco, O. Riglioni, D. |
| author_facet | Ragnisco, O. Riglioni, D. |
| citation_txt | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum / O. Ragnisco, D. Riglioni // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical and dynamical) exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics). We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization.
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| first_indexed | 2025-12-07T16:23:15Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146528 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:23:15Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ragnisco, O. Riglioni, D. 2019-02-09T20:03:32Z 2019-02-09T20:03:32Z 2010 A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum / O. Ragnisco, D. Riglioni // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: (81S10; 81R12; 31C12) DOI:10.3842/SIGMA.2010.097 https://nasplib.isofts.kiev.ua/handle/123456789/146528 A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetry. The high number of symmetries (both geometrical and dynamical) exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics). We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 We wish to thank our colleagues and friends A. Ballesteros, A. Enciso and F.J. Herranz for
 illuminating discussions and crucial suggestions about the content of this paper. The results reported here have been obtained in the framework of the INFN-MICINN collaboration 2010, and the related research activity has been partially supported by the Italian MIUR, through the PRIN 2008 research project n.20082K9KXZ/005. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum Article published earlier |
| spellingShingle | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum Ragnisco, O. Riglioni, D. |
| title | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum |
| title_full | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum |
| title_fullStr | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum |
| title_full_unstemmed | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum |
| title_short | A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum |
| title_sort | family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146528 |
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