J. Phys. I France
Volume 7, Numéro 6, June 1997
Page(s) 749 - 758
DOI: 10.1051/jp1:1997189
J. Phys. I France 7 (1997) 749-758

Algebraic Dynamical Approach to the su(1,1) $\oplus$h(3) Dynamical System: A Generalized Harmonic Oscillator in an External Field

W. Zuo1, 2, 3, 4 and S.J. Wang5, 4

1  Institute of Modern Physics, Academia Sinica, Lanzhou 730000, China
2  Dipartimento di Fisica, University di Catania, Via Corso Italia 57, 95129 Catania, Italy
3  Laboratorio Nazionale del Sud, INFN, 44 Via S. Sofia, 95129 Catania, Italy
4  Department of Modern Physics, Lanzhou University, Lanzhou 730001, China
5  Institute of Modern Physics, Southwest Jiaotong University, Chengdu 610031, China

(Received 27 November 1996, received in final form 17 February 1997, accepted 28 February 1997)

The exact solution and the invariant Cartan operator of the linear nonautonomous system with su(1,1) $\oplus$h(3) dynamical algebra are obtained by using the method of algebraic dynamics. A novel, indirect quantum-classical correspondence of the solutions has been found. It has been shown that algebraic dynamics can be generalized from the linear dynamical system with su(1,1) Lie algebra to a more complicated system with su(1,1) $\oplus$h(3) Lie algebra. Nonadiabatic Berry's phase is also calculated.

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