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Molecular ElectromagnetismA Computational Chemistry Approach$
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Stephan P. A. Sauer

Print publication date: 2011

Print ISBN-13: 9780199575398

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199575398.001.0001

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Perturbation Theory

Perturbation Theory

Chapter:
(p.30) 3 Perturbation Theory
Source:
Molecular Electromagnetism
Author(s):

Stephan P. A. Sauer

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575398.003.0003

This chapter derives the quantum mechanical tools for treating the interaction of molecules with static and dynamic fields, i.e., perturbation theory. The first part is concerned with static fields and presents time-independent perturbation and time-independent response theories. It discusses the Hellmann-Feynman theorem and the general concept of density matrices. The second part considers oscillating fields and develops time-dependent perturbation theory in the form of a time-dependent response theory. The important concept of a response function or polarization propagator is defined and discussed in detail. Expressions for the transition probabilities and rates are also derived and the Ehrenfest and hypervirial theorems are presented.

Keywords:   perturbation theory, response theory, Hellmann-Feynman theorem, Ehrenfest theorem, Hypervirial theorem, transition probabilities, polarization propagator, density matrices

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