  We give a method to compute the smooth part of the density of states in a
semi-classical expansion, when the Hamiltonian contains a Coulomb potential and
non-cartesian coordinates are appropriate. We apply this method to the case of
the hydrogen atom in a magnetic field with fixed $z$-component of the angular
momentum. This is then compared with numerical results obtained by a high
precision finite element approach. The agreement is excellent especially in the
\emph{chaotic} region of the spectrum. The need to go beyond the Thomas-Fermi
model is clearly established.
