Research

• Geometry of Lie groups in Classical and Quantum Mechanics

• Integrability y Superintegrabilty

• Physics on contant curvature spaces

• Cayley-Klein Geometry: models y applications in Physics

Títle: Geometric aspect of the exactly solvable systems  in Quantum and Classical Physics (MTM2005-09183).

Supported by:  Ministerio de Educación y Ciencia

Duration: 2005-2008               

Main researcher: Mariano Santander Navarro

• [FILE] José F. Cariñena, M. F. Rañada and M. Santander: A Quantum Exactly Solvable Nonlinear Oscillator with quasi-Harmonic Behaviour, Preprint 2006

• José F. Cariñena, M. F. Rañada and M. Santander: Lagrangian Conservative approach to two Nonlinear Systems: one-dimensional Integrability and two-dimensional superintegrability, Preprint (2005)

• M. Santander and Teresa Sanz-Gil: From oscillator(s) and Kepler(s) potentials to general superintegrable systems in spaces of constant curvature”, Preprint (2005)

• F. J. Herranz and M. Santander: Relativistic expansions. To appear in Turkish Journal of Physics

• José F. Cariñena, Manuel F. Rañada, y Mariano Santander: A Nonlinear Deformation of the Isotonic Oscillator and the Smorodinski-Winternitz System: Integrability and Superintegrability, Regular and Chaotic Dynamics 10 (2005)

• José F. Cariñena, Manuel F. Rañada, Mariano Santander y Teresa Sanz-Gil: Separable Potentials and a triality in Spaces of constant curvature, J. Nonl. Math. Phys. 12 (2005) 230.

• [FILE] José F. Cariñena, Manuel F. Rañada y Mariano Santander: Lagrangian formalism for nonlinear second-order Riccati systems: one-dimensional integrability and two-dimensional superintegrability,J. Math. Phys. 46 (2005)

• [FILE] José  F. Cariñena, Manuel F. Rañada y Mariano Santander: Central potentials on spaces of constant curvature: The Kepler problem on the twodimensional sphere S2 and the hyperbolic plane H2, J. Math. Phys. 46 (2005) 052702

• [FILE] José  F. Cariñena, Manuel F. Rañada y Mariano Santander: Two important examples of nonlinear oscillators, Procs. of the 10th Int. Conf. in in Modern Group Analysis, Larnaca, Chipre, pp. 39-46, 2004.

• José F. Cariñena, M. F. Rañada and M. Santander:  One-dimensional model of a quantum non-linear harmonic oscillator, Rep. Math. Phys, 54, 375-383 (2004)

• [FILE]  José F. Cariñena, Manuel F. Rañada, Mariano Santander y Murugaian Senthilvelan: A non-linear Oscillator with quasi-Harmonic behaviour: two- and n-dimensional Oscillators, Nonlinearity 17 (2004) 1941.

• [FILE] A. Ballesteros, F. J. Herranz, M. Santander and T. Sanz-Gil : Maximally Smorodinsky-Winternitz systems on the N-dimensional sphere and hyperbolic spaces Superintegrability in Classical and Quantum Systems", edited by P.Tempesta, P.Winternitz, J.Harnad, W.Miller Jr., G.Pogosyan and M.A.Rodriguez, CRM Proceedings & Lecture Notes, vol.37, American Mathematical Society, 2004.

•  R. Ortega, M. Santander: Trigonometry of the Quantum State Space, Geometric Phases and relative Phases. J. Phys. A. 36, 459-485 (2003)

• [FILE] A. Ballesteros, F. J. Herranz, M. Santander and T. Sanz-Gil : Maximal superintegrability on N-dimensional curved spaces J. Phys. A., 36, L93-L99 (2003)

• M. F. Rañada, M. Santander: On harmonic oscillator on the two-dimensional sphere S2 and the hyperbolic plane H2. II, J. Math. Phys., 44, 2149-2167 (2003)

• [FILE] R. Ortega, M. Santander: Trigonometry of ‘complex Hermitian’ type homogeneous symmetric spaces. (J. Phys. A., 35, 7877-7917 (2002))

•  M. F. Rañada, M. Santander: On some properties of the harmonic oscillator on spaces of constant curvature, Rep. on Math. Phys., 49, 335-343 (2002)

•  [FILE] F. J. Herranz, M. Santander: Conformal Compactification and cycle-preserving symmetries of spacetimes. J. Phys. A. 35,6619-6629 (2002)

• F. J. Herranz, M. Santander: Conformal Symmetries of spacetimes. J. Phys. A. 35, 6601-6618 (2002)

• M. F. Rañada, M. Santander: On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2, J. Math. Phys. 43, 431-451 (2002)

•  [FILE] L. J. Boya, A Perelomov and M. Santander: Berry phases in homogeneous Khaler manifolds with linear Hamiltonians. J. Math. Phys., 42, 5130-5142 (2001)

• M. F. Rañada, M. Santander: Complex Euclidean superintegrable potentials, potentials of Drach and potential of Holt, Phys. Lett. A, 278, 271-279 (2001)

• M. Santander: “Matemáticas y Mecánica Cuántica”, Revista Española de Física, 14,5 23-30 (2000)

• [FILE] F. J. Herranz, R. Ortega, M. Santander: Trigonometry of space-times: a new self-dual approach to a curvature/signature (in)dependent trigonometry, J. Phys. A 33 4525-4553 (2000).to a curvature/signature (in)dependent trigonometry, J. Phys. A 33 4525-4553 (2000).

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