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A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum
Репозиторій DSpace/Manakin
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum
Інший ID:
2010 Mathematics Subject Classification: (81S10; 81R12; 31C12)
DOI:10.3842/SIGMA.2010.097
DOI:10.3842/SIGMA.2010.097
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
608
Завантажень:
282
Анотація:
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.
