Mathematical definitions
Pauli exclusion principle (PEP) #
In 1925, Pauli described the PEP for electrons, which states that it is impossible for two electrons of the same atom to simultaneously have the same values of the following four quantum numbers: 
, the principal quantum number; 
, the angular momentum quantum number; 
, the magnetic quantum number; and 
, the spin quantum number.
Following the discovery of various types of elementary particles, the PEP for electrons has been generalized for all elementary particles and composite systems. Remember that fermions are particles that have half-integer spin (
) and bosons are particles that have integer spin (
). The general formulation of the PEP states the total wave function 
for a quantum system must have certain symmetries for all sets of identical particles, that is, electrons and identical nuclei, both bosons and fermions, under the operation of pair particle permutation:
- For fermions, the total wave function must...