Antisymmetrizer

In quantum mechanics, an antisymmetrizer ${\displaystyle {\mathcal {A}}}$ (also known as antisymmetrizing operator) is a linear operator that makes a wave function of N identical fermions antisymmetric under the exchange of the coordinates of any pair of fermions. After application of ${\displaystyle {\mathcal {A}}}$ the wave function satisfies the Pauli principle. Since ${\displaystyle {\mathcal {A}}}$ is a projection operator, application of the antisymmetrizer to a wave function that is already totally antisymmetric has no effect, acting as the identity operator.

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