QUANTUM LC-CIRCUITS WITH A TIME DEPENDENT EXTERNAL SOURCE
Pages 79-86
C. Micu, E. Papp, D. Racolta
Abstract
Starting from the discretization of the electric charge in terms of integer multiples of an elementary charge
leads to the onset of non-Hermitian but conjugated flux operators. Such operators get established in terms of
left- and right-hand discrete derivatives. The Hermitian kinetic energy term can then be readily established
by resorting to the product of flux operators just referred to above. Dealing with the LC-circuit amounts to
consider the influence of quadratic and linear terms in a time dependent discrete Schrödinger-equation.
Such terms are responsible for the magnetic flux and the time-dependent electric field, respectively. One
shows that the electric charge discretization can also be readily described by accounting, in general, for
integer dependent functions instead of the integer referred to above.