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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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The Schrödinger Equation in the Presence of Fields

The Schrödinger Equation in the Presence of Fields

Chapter:
(p.4) (p.5) 2 The Schrödinger Equation in the Presence of Fields
Source:
Molecular Electromagnetism
Author(s):

Stephan P. A. Sauer

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575398.003.0002

This chapter derives the Hamiltonian for the electronic Schrödinger equation of a molecule in the presence of external and internal static electric or magnetic fields. It starts off with the Born-Oppenheimer approximation and discusses in detail the minimal coupling approach to the interaction of molecules with fields from a non-relativistic as well as relativistic point of view. In this context, the Dirac equation of an electron is derived and reduced to the Schrödinger-Pauli equation via the elimination of the small component approach. It also considers the relation between electric and magnetic fields and their scalar and vector potentials through Maxwell's equations, and introduces the problems related to transformations of the gauge of these potentials.

Keywords:   Schrödinger equation, Born-Oppenheimer approximation, minimal coupling, Dirac equation, small component, transformations, Maxwell's equations

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