Generalized versus selected descriptions of quantum LC-circuits

Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F (n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrödingerequation established before via F (n) = n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F (n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed.