Evolution of Quantum State in the Mesoscopic LC Circuit Driven by a Time Dependent Source

We obtained the exact solution of time evolution by applying the Wei-Norman method.The quasi-probability distribution function of phase space is used to investigate the quantum state of the mesoscopic LC circuit in coherent state. The results show that the function of the system is the two dimensional motional gauss wave-packet. The centre charge and flux of the wave-packet vary with cosine and sine wave.