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Mathematics for Physics

130 Pauli Exclusion Principle

A quantum-mechanical rule that is used to forbid two identical fermions from occupying the same quantum state, where a fermion is a particle with half-integer spin, and where a quantum state is a complete set of quantum numbers for one particle.

The exclusion rule. No two electrons can occupy the same state. This principle is used to fill orbitals with at most two electrons of opposite spin.

Antisymmetry of the fermion wavefunction. The many-electron wavefunction must be antisymmetric under exchange of any two electrons. An antisymmetric wavefunction changes sign when two particle labels are swapped. This principle is used to write Slater determinants.

The four one-electron quantum numbers. A complete one-electron label is \((n,\ell,m_{\ell},m_{s})\). This principle is used to count how many electrons fit in a subshell.