Efficient computation of the MCTDHF approximation to the time-dependent Schrödinger equation

Abstract

We discuss analytical and numerical properties of the multi-configuration time-dependent Hartree-Fock method for the approximate solution of the time-dependent multi-particle (electronic) Schrödinger equation which are relevant for an efficient implementation of this model reduction technique. Particularly, we focus on a discretization and low rank approximation in the evaluation of the meanfield terms occurring in the MCTDHF equations of motion, which is crucial for the computational tractability of the problem. We give error bounds for this approximation and demonstrate the achieved gain in performance.

Keywords

• multi-configuration time-dependent Hartree-Fock method
• time-dependent multi-particle Schrödinger equation
• Coulomb potential
• finite elements