# Wave function of IQH and FQH electrons

What are the wave functions of the ground state of Integer Quantum Hall (IQH) and Fractional Quantum Hall (FQH) electrons?

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The Laughlin ones. –  wsc Oct 26 '12 at 1:47

Consider the lowest Landau level, and the simplest FQH state (namely the Laughlin state of 1/3 filling). The IQH ground state wave function is $$\Psi_1=\prod_{i<j}(z_i-z_j)e^{-\frac{1}{4}\sum_i|z_i|^2},$$ and the FQH state wave function is $$\Psi_3=\prod_{i<j}(z_i-z_j)^3e^{-\frac{1}{4}\sum_i|z_i|^2}.$$

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Why is your wavefunction for the IQH state a many-body wavefunction when it is a single-particle phenomena? –  DaniH Oct 30 '12 at 22:23
@DaniH A single-particle phenomenon does not mean that the phenomenon only involves one particle. IQH state is a many-body state, which does have a many-body wave function. –  Everett You Nov 10 '12 at 10:59
The ground state depends on the "filling fraction", which is the number of electrons per flux quanta that thread the 2 dimensional electron gas, $\Psi_1$ is the ground state expected when the filling fraction is exactly 1, that is one electron per flux quanta, $\Psi_3$ is the ground state expected when the filling fraction is 1/3, that is three flux quanta per electron.