Numerical test of disk trial wave function for a half-filled Landau level

The analyticity of the lowest Landau level wave functions and the relation between the filling factor and the total angular momentum severely limits the possible forms of trial wave functions of a disk of electrons subject to a strong perpendicular magnetic field. For the number N of electrons up to 12 we have tested these disk trial wave functions for the half-filled Landau level using Monte Carlo and exact diagonalization methods. The agreement between the results for the occupation numbers and ground state energies obtained from these two methods is excellent. We have also compared the profile of the occupation number near the edge with that obtained from a field-theoretical method. The results give qualitatively identical edge profiles. Experimental consequences are briefly discussed.