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 momentum operators ${P}_{\pm}={P}_{x}\pm i{P}_{y}$ play the role of shift operators. The ${P}_{x}$ and ${P}_{y}$ operators, the third projection of the orbital angular momentum operator ${L}_{z}$ , 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 ${\psi}_{lm}\left(\mathit{r}\right)$ and ${\psi}_{(l\pm 1)(m\pm 1)}\left(\mathit{r}\right)$ .
 Authors:

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 Centro Universitario Valle de Chalco, Universidad Autónoma del Estado de México, 56615 Valle de Chalco Solidaridad, MEX, Mexico
 Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 708034001, USA
 Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 708034001, USA, Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, UPALM, 07738 Mexico, DF 07738, Mexico
 Publication Date:
 Grant/Contract Number:
 SC0005248
 Type:
 Published Article
 Journal Name:
 Advances in Mathematical Physics
 Additional Journal Information:
 Journal Name: Advances in Mathematical Physics Journal Volume: 2014; Journal ID: ISSN 16879120
 Publisher:
 Hindawi Publishing Corporation
 Sponsoring Org:
 USDOE
 Country of Publication:
 Country unknown/Code not available
 Language:
 English
 OSTI Identifier:
 1198290
Sun, GuoHua, Launey, K. D., Dytrych, T., Dong, ShiHai, and Draayer, J. P.. A New Kind of Shift Operators for Infinite Circular and Spherical Wells. Country unknown/Code not available: N. p.,
Web. doi:10.1155/2014/987376.
Sun, GuoHua, Launey, K. D., Dytrych, T., Dong, ShiHai, & Draayer, J. P.. A New Kind of Shift Operators for Infinite Circular and Spherical Wells. Country unknown/Code not available. doi:10.1155/2014/987376.
Sun, GuoHua, Launey, K. D., Dytrych, T., Dong, ShiHai, and Draayer, J. P.. 2014.
"A New Kind of Shift Operators for Infinite Circular and Spherical Wells". Country unknown/Code not available.
doi:10.1155/2014/987376.
@article{osti_1198290,
title = {A New Kind of Shift Operators for Infinite Circular and Spherical Wells},
author = {Sun, GuoHua and Launey, K. D. and Dytrych, T. and Dong, ShiHai and Draayer, J. P.},
abstractNote = {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 ± = P x ± i P y play the role of shift operators. The P x and P y operators, the third projection of the orbital angular momentum operator L z , 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 ψ l m ( r ) and ψ ( l ± 1 ) ( m ± 1 ) ( r ) .},
doi = {10.1155/2014/987376},
journal = {Advances in Mathematical Physics},
number = ,
volume = 2014,
place = {Country unknown/Code not available},
year = {2014},
month = {1}
}