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Intertwining Symmetry Algebras of Quantum Superintegrable Systems
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Intertwining Symmetry Algebras of Quantum Superintegrable Systems
Інший ID:
2000 Mathematics Subject Classification: 17B80; 81R12; 81R15
Посилання:
Intertwining Symmetry Algebras of Quantum Superintegrable Systems / J.A. Calzada, J. Negro, M.A. del Olmo // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 29 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the VIIth Workshop “Quantum Physics with NonHermitian Operators” (June 29 – July 11, 2008, Benasque, Spain). This work has been partially supported by DGES of the Ministerio de Educaci´on y Ciencia of Spain under Project FIS2005-03989 and Junta de Castilla y Le´on (Spain) (Project GR224).
Дата:
2009
Переглядів:
360
Завантажень:
216
Анотація:
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness.
