  We obtain a reduction scheme for the study of the quantum evolution of an
atom in constant magnetic fields using the method developed by Martinez, Nenciu
and Sordoni based on the construction of almost invariant subspace. In
Martinez-Sordoni \cite{MaSo2} such a case is also studied but their reduced
Hamiltonian includes the vector potential terms. In this paper, using the
center of mass coordinates and constructing the almost invariant subspace
different from theirs, we obtain the reduced Hamiltonian which does not include
the vector potential terms. Using the reduced evolution we also obtain the
asymptotic expantion of the evolution for a specific localized initial data,
which verifies the straight motion of an atom in constatnt magnetic fields.
