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 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 Schrdinger-equation established before via F(n)=n. Such generalization

The Hofstadter butterfly’s energy spectrum is discussed both for infinite and finite lattices. For this purpose a square, a triangle and a honeycomb lattice are accounted for. The set of the nested band structures is treated in same more detail.