Exact Solution to Landau System with Time-Dependent Electromagnetic Fields

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 p_y, respectively. The energy of the system, the fluctuations of dynamical variables, the transition amplitudes between different states, and the Berry phase are calculated.