  We construct an explicit duality between the interacting quantum Hall system
in the lowest Landau level and a non-interacting Landau problem. This is done
by absorbing the interaction into the gauge field in the form of an effective
magnetic vector potential. The result is analogous to, and illuminates the
microscopic origin of, the well-known composite fermion model, but has several
advantageous properties. Using this duality we derive, for an arbitrary
short-range interaction, analytic expressions for the ground state energy and
the excitation gap as functions of the filling fraction. We find good agreement
with existing results.
