  Time dependent quantum systems are the subject of intense inquiry, in
mathematics, science, and engineering, particularly at the atomic and molecular
levels. In 1984, Runge and Gross introduced time dependent density functional
theory (TDDFT), a noninteracting electron model, which predicts charge exactly.
An exchange-correlation potential is included in the Hamiltonian to enforce
this property. We have previously investigated such systems on bounded domains
for Kohn-Sham potentials by use of evolution operators and fixed point
theorems. In this article, motivated by use in the physics community, we
consider local density approximations (LDA) for building the
exchange-correlation potential, as part of a set of quantum corrections.
Existence and uniqueness of solutions are established separately within a
framework for general quantum corrections, including time-history potentials
and ionic Coulomb potentials, in addition to general LDA potentials. In
summary, we are able to demonstrate a unique weak solution, on an arbitrary
time interval, for a general class of quantum corrections, including those
typically used in numerical simulations of the model.
