Sistemas superintegrables en espacios homogéneos de SU(p,q)
In this work we have studied different aspects of a family of superintegrable Hamiltonian systems associated with the pseudo-orthogonal groups S(p,q), p + q = n + 1. These systems were obtained by Marsden-Weinstein reduction from a free hamiltonian, no potential term, with configuration space given...
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| Format: | Dissertation |
| Language: | Spanish |
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ProQuest Dissertations & Theses
01-01-2002
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| Online Access: | Get full text |
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| Summary: | In this work we have studied different aspects of a family of superintegrable Hamiltonian systems associated with the pseudo-orthogonal groups S(p,q), p + q = n + 1. These systems were obtained by Marsden-Weinstein reduction from a free hamiltonian, no potential term, with configuration space given by a complex SU(p,q) homogeneous space. After the reduction the resulting SO(p,q) hamiltonian systems are not free: they include a potential term V(s). Among the potentials that appear in this way we can find generalizations of the Posch-Teller and Morse potentials. The above mentioned systems are “maximally” superintegrable, i.e. they have 2n − 1 functionally independent integrals of motion, not all of them in involution, defined in the phase space of an n-dimensional configuration space. The supeintegrability property is related to the separation of variables of the Hamilton-Jacobi equation in more than one coordinate system. Since the original Hamiltonian are associated with a group we have studied the “contracted” system that must be linked with the corresponding group obtained by a Inonu-Wigner contraction. Finally we have studied the one dimensional quantum mechanical version of these hamiltonians by means of the factorization method. |
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| ISBN: | 9780493539423 0493539425 |