Exact exchange-correlation potential for a time-dependent two electron system
Abstract
We obtain an exact solution of the time-dependent Schroedinger equation for a two-electron system confined to a plane by an isotropic parabolic potential whose curvature is periodically modulated in time. From this solution we compute the exact time-dependent exchange correlation potential vxc which enters the Kohn-Sham equation of time-dependent density functional theory. Our exact result provides a benchmark against which various approximate forms for vxc can be compared. Finally vxc is separated in an adiabatic and a pure dynamical part and it is shown that, for the particular system studied, the dynamical part is negligible.
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