Fermi hole

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The Fermi hole is a physical effect that describes that two electrons with the same spin can never be found in the same place.

Since the overall wave function must be antisymmetric ( Pauli principle ) and the spin component is symmetrical here, the spatial portion of the overall wave function must be antisymmetric. However, if one considers the limit , in which the same coordinates are used for both electrons, the spatial component disappears and the total wave function is zero at this point. From a magnetic point of view, the parallel is the more unfavorable state than the anti-parallel. However, the occurrence of the Fermi hole causes the electrons to get out of the way and the repulsive Coulomb interaction is weakened. The Coulomb effect is far stronger than the magnetic effect.

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In quantum chemistry , numerical calculations are used to describe multi-electron systems (e.g. atoms with atomic number> 1, molecules). The Schrödinger equation can then no longer be solved analytically.

The best known method is Hartree-Fock , also known as the “method of self-consistent fields”. In this case, the interaction of a particulate electron with the average E-field of all other electrons is calculated iteratively.

The biggest mistake of the Hartree-Fock method is that the so-called electron correlation is not taken into account. The gold question is: What happens when two electrons are in the same place at the same time?

This is exactly where the terms "Fermi hole" (English Fermi hole) and " Fermi heap " (English Fermi heap) come into play. The Fermi hole refers to the case that two electrons with the same spin meet. The probability of finding electron 2 in the same place at the same time as electron 1 is zero.

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