@article {Papp:2010-02-01T00:00:00:1546-1955:479,
author = "Papp, E. and Micu, C. and Borchin, O.",
title = "Generalized versus Selected Descriptions of Quantum *LC*-Circuits",
journal = "Journal of Computational and Theoretical Nanoscience",
volume = "7",
number = "2",
year = "2010-02-01T00:00:00",
abstract = "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 SchrÃ¶dinger-equation 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.",
pages = "479-485",
url = "http://www.ingentaconnect.com/content/asp/jctn/2010/00000007/00000002/art00019",
doi = "doi:10.1166/jctn.2010.1382",
keyword = "QUANTUM LC-CIRCUITS, CHARGE DISCRETIZATION, DISCRETE SCHRÃ–DINGER EQUATIONS, MANY-CHARGE GENERALIZATIONS"
}