Abstract or Additional Information
Abstract: The talk analyzes a general version of time dependent quantum
mechanics, introduced in 1984 by E. Runge and E.K.U. Gross.
The nonlinear system is analyzed by the evolution operators,
introduced by T. Kato in the 1970s. The talk discusses closed
quantum systems, corresponding to homogeneous Dirichlet boundary
conditions on a bounded domain. The existence of a unique weak
solution on a given finite time interval is demonstrated. This
part of the talk is based upon a 2015 publication. We also
discuss some unpublished work relating to the convergence of
operator Newton iteration. This is based upon the fixed point
map, used to establish existence/uniqueness.