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Phys. Rev. A 53, 3691 - 3693 (1996)

Time-dependent quantum systems and the invariant Hermitian operator

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Y.-Z. Lai
Department for Basic Courses, Taiyuan Heavy Machinery Institute, Taiyuan, Shanxi, 030 024, People's Republic of China

J.-Q. Liang
Department of Physics, University of Kaiserslautern, D-67653 Kaiserslautern, Germany
Institute of Theoretical Physics, Shanxi University, Taiyuan, Shanxi 030 006
Institute of Physics, Academia Sinica, Beijing 100 080, People's Republic of China

H. J. W. Müller-Kirsten and J.-G. Zhou
Department of Physics, University of Kaiserslautern, D-67653 Kaiserslautern, Germany

Received 18 December 1995

We study the time evolution of quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators. The invariant Hermitian operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. With the help of the invariant Hermitian operator we obtain not only the exact solutions of the Schrödinger equation but also the time-evolution operator. The adiabatic and nonadiabatic Berry phases are calculated with the exact solutions. © 1996 The American Physical Society.


©1996 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.53.3691
DOI: 10.1103/PhysRevA.53.3691
PACS: 42.50.Dv, 03.65.Bz, 03.65.Fd

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