### 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discuss some unpublished work relating to the convergence of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.