Title page for ETD etd-04132000-13040037


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
Hagedorn, George A. Committee Chair
Beattie, Christopher A. Committee Member
Chang, Lay Nam Committee Member
Klaus, Martin Committee Member
Kohler, Werner E. Committee Member
Keywords
  • molecules
  • Franck-Condon factors
  • electromagnetic field
  • perturbation theory
  • laser
  • 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 Schrodinger equation. Using previous

results that develop asymptotic series solutions

in the Born-Oppenheimer parameter ε, we

derive a formal Dyson series expansion in the

perturbation parameter μ, 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

μ, 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.

Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
  etd.pdf 369.92 Kb 00:01:42 00:00:52 00:00:46 00:00:23 00:00:01

Browse All Available ETDs by ( Author | Department )

dla home
etds imagebase journals news ereserve special collections
virgnia tech home contact dla university libraries

If you have questions or technical problems, please Contact DLA.