In the quantum mechanical modelling of electrons the Coulomb potential in the one particle Schrödinger-Poisson model should be corrected because of "exchange interaction" due to the Pauli principle.

We present a rigorous derivation of the local "Slater approximation" that works also for deriving local density approximation for the kinetic energy, as given in the Thomas-Fermi-von-Weizsäcker model.

Our method is based on deformations (local scaling transformations) of plane waves in a periodic box.

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