Q:

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?

A:

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
$$\Psi_3=\prod_{i<j}(z_i-z_j)^3e^{-\frac{1}{4}\sum_i|z_i|^2}.$$

