Type of Document	Dissertation
Author	Kargol, Armin
URN	etd-03022006-093405
Title	The Born-Oppenheimer approximation in scattering theory
Degree	PhD
Department	Mathematical Physics
Advisory Committee	Advisor Name Title Hagedorn, George A. Committee Chair Bowden, Robert L. Committee Member Klaus, Martin Committee Member Slawny, Joseph Committee Member Zweifel, Paul F. Committee Member
Keywords	Born approximation
Date of Defense	1994-05-05
Availability	restricted
Abstract We analyze the Schrödinger equation i€2∂/∂tΨ = H(€)Ψ, where H(€) = - f24 Δx + h(X) is the hamiltonian of a molecular system consisting of nuclei with masses of order €-4 and electrons with masses of order 1. The Born-Oppenheimer approximation consists of the adiabatic approximation to the motion of electrons and the semiclassical approximation to the time evolution of nuclei. The quantum propagator associated with this Schrödinger Equation is exp(-itH(€)/€2). We use the Born-Oppenheimer method to find the leading order asymptotic expansion in € to exp(_it~(t:»Ψ, i.e., we find Ψ(t) such that: (1) We show that if H(€) describes a diatomic Molecule with smooth short range potentials, then the estimate (1) is uniform in time; hence the leading order approximation to the wave operators can be constructed. We also comment on the generalization of our method to polyatomic molecules and to Coulomb systems.
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