A QUANTUM-MECHANICAL MODEL FOR AN LC CIRCUIT WITH ELASTIC CAPACITOR

Abstract

In this paper, we consider a quantum-mechanical LC circuit connected to a periodic source and with elastic capacitor. In the limit of negligible inductor energy, we present explicitly an exact solution for the wave function and spectrum of the spring-capacitor-source system. Considering the inductor energy as a perturbative term, the time-dependent probability amplitudes for the complete system are derived. We show that the mechanical degrees of freedom lead a suppression of the capacitor's charging/discharging process. Finally, we show the existence of a class of memristive component due to charge discreteness.