title: Functional differentiability in time-dependent quantum mechanics.
abstract: In this work, we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave functions, Fréchet differentiability is proven. From this follows an estimate for the difference of two solutions to the time-dependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the one-particle density and to bounded operators, and present a rigorous formulation of non-equilibrium linear-response theory where the usual Lehmann representation of the linear-response kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of time-dependent density-functional theory.
authors.affiliation: Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Markus
authors.initials: M
authors.lastname: Penz
authors.affiliation: Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Michael
authors.initials: M
authors.lastname: Ruggenthaler