Lie-algebraic description of the quantum superintegrable Smorodinsky-Winternitz system in n dimensions

We apply the potential group method to a family of n-dimensional quantum Smorodinsky-Winternitz systems. The Hamiltonians of the systems are associated with first-order Casimir operators of the unitary group U(3n) restricted to certain subspaces of carrier space of the symmetric representation. Henc...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 45; no. 18; pp. 185201 - 13
Main Author Kerimov, G A
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 11.05.2012
IOP
Subjects
Carriers
Exact sciences and technology
Group theory
Integrals
Mathematical analysis
Operators
Physics
Representations
Strength
Subgroups
Subspaces
Quantum system
U groups
Hamiltonians
First order
Casimir operators
Subgroup
Hamiltonian system
Integrable systems
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Summary:We apply the potential group method to a family of n-dimensional quantum Smorodinsky-Winternitz systems. The Hamiltonians of the systems are associated with first-order Casimir operators of the unitary group U(3n) restricted to certain subspaces of carrier space of the symmetric representation. Hence, the group U(3n) describes fixed energy states of a family of Smorodinsky-Winternitz systems with different potential strength. Moreover, it is shown that 2n − 1 integrals of motions (including the Hamiltonian) are related to Casimir operators of U(3n) and its subgroups.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/18/185201