  We investigate the ground state properties of a two-dimensional electron gas
in the lowest Landau level using the Density Matrix Renormalization Group. The
electron gas is confined to a cylinder with a strong magnetic field
perpendicular to the surface. For a thin cylinder, the ground state is for
generic filling factors a charge density wave state, however, at $\nu=1/2$ a
homogeneous and apparently gapless ground state is found and particle and hole
excitations are studied.
