Type of Document	Dissertation
Author	Jilcott, Jr., Steven Wayne
URN	etd-04132000-13040037
Title	Time-Dependent Perturbation and the Born-Oppenheimer Approximation
Degree	PhD
Department	Physics
Advisory Committee	Advisor Name Title George Hagedorn Committee Chair Christopher Beattie Committee Member Lay Nam Chang Committee Member Martin Klaus Committee Member Werner Kohler Committee Member
Keywords	laser perturbation theory electromagnetic field Franck-Condon factors molecules Born-Oppenheimer approximation
Date of Defense	2000-03-09
Availability	unrestricted
Abstract We discuss the physical problem of a molecule interacting with an electromagnetic field pulse and model the problem using a time-dependent perturbation of the Born-Oppenheimer approximation to the Schr"odinger equation. Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter $epsilon$, we derive a formal Dyson series expansion in the perturbation parameter $mu$, which is proportional to the electromagnetic field strength. We then prove that this series is asymptotically accurate in both parameters, provided that the Hamiltonian for the electrons has purely discrete spectrum. Under more general hypotheses, we show that the series is accurate to first order in $mu$, and that it is accurate to one higher order if we place conditions on the abruptness of the EM pulse. We also show how this series development provides a justification for the Franck-Condon factors in the case of a diatomic molecule.
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