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Pauli principle

The Pauli principle - or "Pauli ban" as well as "Pauli's exclusion principle" - is a law from physics, more precisely one from the field of quantum physics. The discovery of the Pauli principle goes back to the Austrian scientist Wolfgang Ernst Pauli, who used it to formulate one of the most fundamental principles of quantum mechanics in 1925.

Little reminder: Quantum mechanics deals with the laws and states of matter and how their physical properties can be calculated (at the size of atoms and below). This makes the Pauli principle particularly relevant for chemistry.

Pauli Principle: A Definition

Basically, the definition of the Pauli principle lies beyond the norms that apply in classical physics. This assumes that it is never possible to determine whether two particles in an atom are in the same place or not. The logical consequence: They are initially indistinguishable.
Experiments have shown that for orbitals (extended regions containing several particles) a certain probability can be determined to calculate where the electrons are in them. The areas occasionally overlap, so the particles can also be in the same place.

This is where the Pauli principle of physics comes into play: Two electrons can never have the same quantum numbers. These measures of the motion properties of an electron provide information about orbital, angular momentum and spin.
The Pauli principle states that two electrons must differ in at least one of their quantum numbers. It therefore applies to all particles with half-integer spin – called fermions. In addition to electrons, this also includes protons and neutrons.
So-called bosons, which are responsible for the transmission of forces, are not subject to the Pauli principle.

The total wave function of a system of n fermions is antisymmetric with respect to the exchange of two particles:

are the location and is of the spin orientation of the i-th fermion. Furthermore, P is the permutation operator, which causes the exchange of two particles, so the formula is obtained:

.

The consequence of the Pauli principle

By characterizing the fermions in the Pauli principle, it can be shown that only two electrons can find space outside the atomic nucleus in an orbital. From today's point of view this means: If identical fermions are exchanged, the wave function of a quantum system becomes antisymmetric. In this way, precise conclusions can be drawn about the structure and differentiation (periodic table) of matter.
In addition, the exchange interaction of the electrons, which defines the Pauli principle, is responsible for the magnetism.

Exact interpretation of the Pauli rule

The total antisymmetric of a wave function means that it changes sign when any two particles are interchanged.
In physics, antisymmetric means that two fermions can never occupy the same quantum state: If two fermions have the same location and spin quantum number, a formal exchange of the two fermions does not change the wave function - because they are indistinguishable. The only solution is then a vanishing total wave function due to Ψ = − Ψ, i.e.Ψ = 0.

In the case of a separation into position wave function and spin wave function, the antisymmetric of the overall wave function with a symmetrical position wave function requires an antisymmetric spin wave function – and vice versa. An (anti)symmetric spin wave function indicates a pairwise (anti)parallel spin orientation. You get the trivial solution of an antisymmetric spatial wave function if the elementary particles that are exchanged in pairs are in the same place ().