See also: [[Fermi Levels]], http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html # Pauli Exclusion Principle Motivation: Filling in gaps on the graph The Pauli Exclusion Principle States that no two electrons (or more generally [[fermions]]) in an atom can have identical [[quantum number]]s. For two two electrons, 1 and 2 in states $a$ and $b$, the [[nuclear wave function|wave function]] would be $ \psi = \psi_1(a)\psi_2(b) $ where $\psi_1(a)$ is the probability that electron 1 is in state $a$, and $\psi_2(b)$ is the probability that electron 2 is in state $b$. This would imply that $\psi$ is the probability of both states being true. However, this cannot hold because the electrons are identical and thus indistinguishable. Instead, the wave function is a LINEAR COMBINATION of the states: $ \psi = \psi_1(a)\psi_2(b) \pm \psi_1(b)\psi_2(a) $ This now implies that $\psi$ is the probability amplitude that both states $a$ and $b$ are occupied by electrons 1 and 2 in EITHER ORDER. The $+$ is required for [[Bosons]] and $-$ is for [[fermions]].