The Variational Splitting Method for the Multi-Configuration Time-Dependent Hartree-Fock Equations for Atoms

O. Koch
Institute for Analysis and Scientific Computing (E101),
Vienna University of Technology,
Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
Received 6 February, 2009; accepted in revised form 20 December, 2011
Abstract: We discuss the numerical approximation of the solution to the multi-
configuration time-dependent Hartree-Fock (MCTDHF) equations in quantum dynamics.
The associated equations of motion, obtained via the Dirac-Frenkel time-dependent varia-
tional principle, consist of a coupled system of low-dimensional nonlinear partial differential
equations and ordinary differential equations. We extend the analysis of the convergence
of a time integrator based on splitting of the vector field for systems of unbound fermions
to the case where a nuclear attractive potential is present. First order convergence in the
H 1 norm and second order convergence in L2 are established. The analysis applies to
electronic states whose density vanishes at the nucleus.


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