Abstract: By using the technique of integration within ordered product (IWOP) of operators, the time-evolution operator can be expressed as the quantum image of the classical transformation in the coordinate and the momentum phase space. The quantized mesoscopic LCR (resistance, capacitance and inductance) electric circuit and the corresponding Hamiltonian are obtained according to the way of the quantized mesoscopic LC electric circuit. By means of theoretic calculations, it is shown that there exists squeezing mechanism in the quantized mesoscopic LCR electric circuit. Furthermore，the concrete form of the squeezed state in the quantized mesoscopic LCR electric circuit is derived based on the IWOP technique and the quantum Fresnel transformation.

Key words: quantum optics, IWOP integration method, Fresnel operator, squeezed state, quantized mesoscopic LCR