Dynamical symmetries for superintegrable quantum systems

Journal Article · Thu Mar 15 00:00:00 EDT 2007 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778807030088· OSTI ID:21075922

Negro, J; Olmo, M A. del , ^[1]

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1. Universidad de Valladolid, Departmento de Fisica Teorica (Spain)

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are obtained by generalizing the techniques of factorization of one-dimensional systems. We firstly obtain a pair of noncommuting Lie algebras su(2) that originate the algebra so(4). By considering three spherical coordinate systems, we get the algebra u(3) that can be enlarged by 'reflexions' to so(6). The bounded eigenstates of the Hamiltonian hierarchies are associated to the irreducible unitary representations of these dynamical algebras.

• OSTI ID: 21075922
• Journal Information: Physics of Atomic Nuclei, Vol. 70, Issue 3; Other Information: DOI: 10.1134/S1063778807030088; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
EIGENSTATES
FACTORIZATION
HAMILTONIANS
LIE GROUPS
MATHEMATICAL OPERATORS
ONE-DIMENSIONAL CALCULATIONS
REDUCTION
SO-4 GROUPS
SO-6 GROUPS
SPHERICAL CONFIGURATION
SU-2 GROUPS
SYMMETRY
TWO-DIMENSIONAL CALCULATIONS
U-3 GROUPS