We present a quantum description of a mesoscopic RLC circuit. Based on the Caldirola-Kanai Hamiltonian and quantum invariant method we solve the Schrödinger equation for this circuit and write the corresponding wave functions in terms of a particular solution of the Milne-Pinney equation. In addition, we construct coherent and squeezed states for the quantized RLC circuit and evaluate the quantum fluctuations of the charge and the magnetic flux as well as the uncertainty product. Subject Index: 060, 064 The study of mesoscopic systems has attracted a lot of attention in the litera-ture in the last few years.1)–19) The great interest in these systems is motived partly because of the rapid development of nanophysics and nanoelectronics and partly because in the manufacture of electronics devices the miniaturization of integrated