= Slater determinant
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{title2=$\Psi(x_1,\ldots,x_N)=\det\!\left[u_j(x_i)\right]/\sqrt{N!}$}
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A <Slater determinant> extends <two-particle antisymmetrization> to $N$ <fermions>. Here $x_i$ contains position and <spin> or other internal variables. Distinct <orthonormal> <one-particle states> give the normalized <wavefunction> displayed in the title. Repeating a <one-particle state> repeats a column of the <determinant>, so the <wavefunction> vanishes. Exchanging particle slots exchanges rows and reverses its sign. A general <fermionic> <quantum state> can be a <quantum superposition> of <Slater determinants>; it need not be one <Slater determinant>.
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