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 phi = -E(t)y +k(t)y(2), 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 harmoni c oscillator with a moving origin and a varying amplitude of width, the par amertes of the gauge transformation are related to the amplitude, the veloc ity potential and the expectations of y and p(y), respectively. The energy of the system, the fluctuations of dynamical variables, the transition ampl itudes between different states, and the Berry phase are calculated.