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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Bibliographic Details
Published inAdvances in Mathematical Physics Vol. 2014; no. 2014; pp. 765 - 771
Main Authors Sun, Guo-Hua, Launey, K. D., Dytrych, T., Dong, Shi-Hai, Draayer, Jerry
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Analysis
Coordinate transformations
Mathematical problems
Quantum mechanics
Transformations (Mathematics)
Variables
United States
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Summary: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).
ISSN:1687-9120
1687-9139
DOI:10.1155/2014/987376