Born-Oppenheimer approximation for an atom in constant magnetic fields (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

We announce our recent results about a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields by the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Using the center of mass coordinates and constructing the almost invariant subspace different from that of Martinez and Sordoni, 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.