The mesoscopic RLC circuit with a alternationg voltage source was discussed by quantum invariant theory. The mutual-couple energe and the dissipation were also taken into account. The Hamiltonian of the mesoscopic system was derived from Lagrangian function. The wave function of the system will evolve to a squeezed state as time elapses. In conclusion,the state of the system will evolve from a arbitrary initial state to a general squeezed state.