Pauli exclusion principle
The Pauli exclusion principle states that fermions
are antisymmetric under particle exchange, and that as a consequence no two fermions may occupy the same quantum state.
Mathematically, the exchange operator for a two-body wavefunction is
Normalisation considerations tell us that the eigenvalue,
must be either
(as the operator
must conserve probability).
The Pauli exclusion principle then states that the eigenvalue is
for bosons
and
for fermions, and that a wavefunction with an eigenvalue of
describes particles that cannot occupy the same quantum state. The spin-statistics theorem
states that these particles are fermions, with half-integer spin.
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