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Exact Solution to Landau System with Time-Dependent Electromagnetic Fields |
| YING Zu-jian1;WANG Shun-jin1,2;ZHANG Wen-zhong1 |
| 1Department of Modern Physics, Lanzhou University, Lanzhou 730000
1Institute of Modern Physics, Southwest Jiaotong University, Chengdu 610031
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| Cite this article: |
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YING Zu-jian, WANG Shun-jin, ZHANG Wen-zhong 1999 Chin. Phys. Lett. 16 391-393 |
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Abstract Algebraic dynamics is applied to treat Landau system. We consider the case with the vector potential A = B(t)(-y, 0,0) and the scalar potential Ф = -E(t)y +k(t)y2, and find that the system has the dynamical algebra su (1,1) h (3). With a gauge transformation the exact solutions of the system are found, of which the quantum motion in y-direction represents a harmonic oscillator with a moving origin and a varying amplitude of width, the paramertes of the gauge transformation are related to the amplitude, the velocity potential and the expectations of y and py, respectively. The energy of the system, the fluctuations of dynamical variables, the transition amplitudes between different states, and the Berry phase are calculated.
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03.65.Fd
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Published: 01 June 1999
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