Born-Oppenheimer Approximation for an Atom in Constant Magnetic Fields

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 and Sordoni (Mem AMS 936, 2009) 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 of the nucleus. Using the reduced evolution, we also obtain the asymptotic expansion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constant magnetic fields.