Talk:PlanetPhysics/Pauli Exclusion Principle

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%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: Pauli exclusion principle %%% Primary Category Code: 10. %%% Filename: PauliExclusionPrinciple.tex %%% Version: 1 %%% Owner: invisiblerhino %%% Author(s): invisiblerhino %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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The Pauli exclusion principle states that \htmladdnormallink{fermions}{http://planetphysics.us/encyclopedia/AntiCommutationRelations.html} are antisymmetric under \htmladdnormallink{particle}{http://planetphysics.us/encyclopedia/Particle.html} 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 \[ \hat{X} \psi(1, 2) = g \psi(2, 1) \] Normalisation considerations tell us that the eigenvalue, $g$ must be either $\pm 1$ (as the \htmladdnormallink{operator}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} must conserve probability). The Pauli exclusion principle then states that the eigenvalue is $+1$ for \htmladdnormallink{bosons}{http://planetphysics.us/encyclopedia/Boson.html} and $-1$ for fermions, and that a wavefunction with an eigenvalue of $-1$ describes particles that cannot occupy the same quantum state. The spin-statistics \htmladdnormallink{theorem}{http://planetphysics.us/encyclopedia/Formula.html} states that these particles are fermions, with half-integer \htmladdnormallink{spin}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html}.

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