Laughlin wavefunction

Summary

The Laughlin wavefunction is a trial ground state for the fractional quantum Hall effect at filling fractions $\nu = 1/m$, $m$ odd. Robert Laughlin proposed it in 1983. It is a product of the factors $(z_i - z_j)^m$ over all pairs of electrons, times a Gaussian. Here $z_j$ is the position of electron $j$ as a complex number. Its excitations carry fractional charge $e/m$ and have fractional exchange statistics, so they are anyons. Laughlin shared the 1998 Nobel Prize in Physics for this explanation.