Slater determinant

In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions).[1] Only a small subset of all possible fermionic wave functions can be written as a single Slater determinant, but those form an important and useful subset because of their simplicity.

The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital , where denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere.

The Slater determinant is named for John C. Slater, who introduced the determinant in 1929 as a means of ensuring the antisymmetry of a many-electron wave function,[2] although the wave function in the determinant form first appeared independently in Heisenberg's[3] and Dirac's[4][5] articles three years earlier.

  1. ^ Molecular Quantum Mechanics Parts I and II: An Introduction to QUANTUM CHEMISTRY (Volume 1), P. W. Atkins, Oxford University Press, 1977, ISBN 0-19-855129-0.
  2. ^ Slater, J. (1929). "The Theory of Complex Spectra". Physical Review. 34 (2): 1293–1322. Bibcode:1929PhRv...34.1293S. doi:10.1103/PhysRev.34.1293.
  3. ^ Heisenberg, W. (1926). "Mehrkörperproblem und Resonanz in der Quantenmechanik". Zeitschrift für Physik. 38 (6–7): 411–426. Bibcode:1926ZPhy...38..411H. doi:10.1007/BF01397160. S2CID 186238286.
  4. ^ Dirac, P. A. M. (1926). "On the Theory of Quantum Mechanics". Proceedings of the Royal Society A. 112 (762): 661–677. Bibcode:1926RSPSA.112..661D. doi:10.1098/rspa.1926.0133.
  5. ^ "Slater determinant in nLab". ncatlab.org. Retrieved 2023-11-08.