A Slater determinant extends two-particle antisymmetrization to fermions. Here 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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A Slater determinant is a mathematical construct used in quantum mechanics to describe the wavefunction of a system of identical fermions, such as electrons. It is named after the physicist John C. Slater, who introduced this technique. Fermions are particles that follow the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. A Slater determinant provides a way to construct a many-body wavefunction that inherently respects this principle.
