The infinite time limit for the time-dependent Born-Oppenheimer approximation |
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| Authors: | Armin Kargol |
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| Institution: | (1) Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, 24061 Blacksburg, Va, USA;(2) Present address: IMA, University of Minnesota, 55455 Minneapolis, MN |
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| Abstract: | We analyze the Schrödinger equation
, whereH( ) is the hamiltonian of the molecular system consisting of nuclei with masses proportional to –4 and electrons with masses of order 1. Using the Born-Oppenheimer method we construct the leading order asymptotic expansion to the exact solutions of the equation. We show that if the particles interact through smooth potentials decaying suitably as the distance between particles tends to  , then the expansion holds uniformly for all timest 0,). By similar analysis one can show validity of the expansion fort(–,0], thus our results hold for scattering theory.The material in this paper is contained in a dissertation submitted to the faculty of VPI & SU in partial fulfillment of the requirements for the Ph.D. degree. |
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