Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction

Bach, Volker; Breteaux, Sébastien; Petrat, Sören; Pickl, Peter and Tzaneteas, Tim (2016): Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. In: Journal De Mathematiques Pures et Appliquees, Vol. 105, No. 1: pp. 1-30

Abstract

We study the time evolution of a system of N spinless fermions in R-3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrodinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system. (C) 2015 The Authors. Published by Elsevier SAS. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0021-7824
• Language: English