  This paper deals with the comparison between the strong Thomas-Fermi theory
and the quantum mechanical ground state energy of a large atom confined to
lowest Landau band wave functions. Using the tools of microlocal semiclassical
spectral asymptotics we derive precise error estimates. The approach presented
in this paper suggests the definition of a modified strong Thomas-Fermi
functional, where the main modification consists in replacing the integration
over the variables perpendicular to the magnetic field by an expansion in
angular momentum eigenfunctions. The resulting DSTF theory is studied in detail
in the second part of the paper.
