  The Schrodinger equation for an interacting spinless electron gas in a
nonuniform magnetic field admits an exact solution in Jastrow product form when
the fluctuations in the magnetic field track the fluctuations in the scalar
potential. For tracking realizations in a two-dimensional electron gas, the
degeneracy of the lowest Landau level persists, and the ``tracking'' solutions
span the ground state subspace. In the context of the fractional quantum Hall
problem, the Laughlin wave function is shown to be a tracking solution.
Tracking solutions for screened Coulomb interactions are also constructed. The
resulting wavefunctions are proposed as variational wave functions with
potentially lower energy in the case of non-negligible Landau level mixing than
the Laughlin function.
