The authors quantize the mesoscopic RLC circuit with the help of the canonical transformation, define the coherent state of the mesoscopic RLC circuit, and investigate the quantum fluctuatio ns of the charge and current of the circuit in this coherent state.Some useful r esults are obtained.
The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as well as the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.