A New Kind of Shift Operators for Infinite Circular and Spherical Wells
A new kind of shift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii R sharing energy levels with a common eigenvalue. In circular well, the...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/987376 |
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| author | Guo-Hua Sun K. D. Launey T. Dytrych Shi-Hai Dong J. P. Draayer |
| author_facet | Guo-Hua Sun K. D. Launey T. Dytrych Shi-Hai Dong J. P. Draayer |
| author_sort | Guo-Hua Sun |
| collection | DOAJ |
| description | A new kind of shift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii R sharing energy levels with a common eigenvalue. In circular well, the momentum operators P±=Px±iPy play the role of shift operators. The Px and Py operators, the third projection of the orbital angular momentum operator Lz, and the Hamiltonian H form a complete set of commuting operators with the SO(2) symmetry. In spherical well, the shift operators establish a novel relation between ψlm(r) and ψ(l ± 1)(m±1)(r). |
| format | Article |
| id | doaj-art-2501ef834bb4469f88b0fd7aab2efa97 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2501ef834bb4469f88b0fd7aab2efa972025-02-03T05:52:50ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/987376987376A New Kind of Shift Operators for Infinite Circular and Spherical WellsGuo-Hua Sun0K. D. Launey1T. Dytrych2Shi-Hai Dong3J. P. Draayer4Centro Universitario Valle de Chalco, Universidad Autónoma del Estado de México, 56615 Valle de Chalco Solidaridad, MEX, MexicoDepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USADepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USADepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USADepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USAA new kind of shift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii R sharing energy levels with a common eigenvalue. In circular well, the momentum operators P±=Px±iPy play the role of shift operators. The Px and Py operators, the third projection of the orbital angular momentum operator Lz, and the Hamiltonian H form a complete set of commuting operators with the SO(2) symmetry. In spherical well, the shift operators establish a novel relation between ψlm(r) and ψ(l ± 1)(m±1)(r).http://dx.doi.org/10.1155/2014/987376 |
| spellingShingle | Guo-Hua Sun K. D. Launey T. Dytrych Shi-Hai Dong J. P. Draayer A New Kind of Shift Operators for Infinite Circular and Spherical Wells Advances in Mathematical Physics |
| title | A New Kind of Shift Operators for Infinite Circular and Spherical Wells |
| title_full | A New Kind of Shift Operators for Infinite Circular and Spherical Wells |
| title_fullStr | A New Kind of Shift Operators for Infinite Circular and Spherical Wells |
| title_full_unstemmed | A New Kind of Shift Operators for Infinite Circular and Spherical Wells |
| title_short | A New Kind of Shift Operators for Infinite Circular and Spherical Wells |
| title_sort | new kind of shift operators for infinite circular and spherical wells |
| url | http://dx.doi.org/10.1155/2014/987376 |
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