Functional differentiability in timedependent quantum mechanics
Abstract
In this work, we investigate the functional differentiability of the timedependent manybody wave function and of derived quantities with respect to timedependent 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 timedependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the oneparticle density and to bounded operators, and present a rigorous formulation of nonequilibrium linearresponse theory where the usual Lehmann representation of the linearresponse kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of timedependent densityfunctional theory.
 Authors:
 Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck (Austria)
 Publication Date:
 OSTI Identifier:
 22415556
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BANACH SPACE; DENSITY FUNCTIONAL METHOD; EQUILIBRIUM; KERNELS; MANYBODY PROBLEM; MATHEMATICAL SOLUTIONS; PARTICLES; POTENTIALS; QUANTUM MECHANICS; SCHROEDINGER EQUATION; TIME DEPENDENCE; WAVE FUNCTIONS
Citation Formats
Penz, Markus, Email: markus.penz@uibk.ac.at, and Ruggenthaler, Michael, Email: michael.ruggenthaler@uibk.ac.at. Functional differentiability in timedependent quantum mechanics. United States: N. p., 2015.
Web. doi:10.1063/1.4916390.
Penz, Markus, Email: markus.penz@uibk.ac.at, & Ruggenthaler, Michael, Email: michael.ruggenthaler@uibk.ac.at. Functional differentiability in timedependent quantum mechanics. United States. doi:10.1063/1.4916390.
Penz, Markus, Email: markus.penz@uibk.ac.at, and Ruggenthaler, Michael, Email: michael.ruggenthaler@uibk.ac.at. 2015.
"Functional differentiability in timedependent quantum mechanics". United States.
doi:10.1063/1.4916390.
@article{osti_22415556,
title = {Functional differentiability in timedependent quantum mechanics},
author = {Penz, Markus, Email: markus.penz@uibk.ac.at and Ruggenthaler, Michael, Email: michael.ruggenthaler@uibk.ac.at},
abstractNote = {In this work, we investigate the functional differentiability of the timedependent manybody wave function and of derived quantities with respect to timedependent 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 timedependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the oneparticle density and to bounded operators, and present a rigorous formulation of nonequilibrium linearresponse theory where the usual Lehmann representation of the linearresponse kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of timedependent densityfunctional theory.},
doi = {10.1063/1.4916390},
journal = {Journal of Chemical Physics},
number = 12,
volume = 142,
place = {United States},
year = 2015,
month = 3
}

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