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 t he 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 Land au level using Monte Carlo and exact diagonalization methods. The agreement between the results for the occupation numbers and ground state energies o btained from these two methods is excellent. We have also compared the prof ile 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.