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Magnetic, Electric, and Mechanical Properties of Polymers

  • János J. Ladik

Abstract

If we neglect interaction of the electronic and/or nuclear spins with an external magnetic field (which can be treated correctly only within the framework of a relativistic CO theory; see Section 1.5), the one-electron Hamiltonian of a system in the presence of a magnetic field H can be written in the form
$$\overset{x}{\mathop{H}}\,=\frac{\overset{\wedge }{\mathop{p}}\,}{2m}+V(r)$$
(10.1)
where
$$\overset{\wedge }{\mathop{p}}\,=\overset{\wedge }{\mathop{p}}\,-\frac{e}{c}A;\,H(r)=curlA(r)$$
(10.2)
In the Hartree-Fock case one can then write
$$\overset{\wedge }{\mathop{F}}\,=\overset{x}{\mathop{{{H}^{N}}}}\,+\sum\limits_{j}{(2\overset{\wedge }{\mathop{{{J}_{j}}}}\,-\overset{\wedge }{\mathop{{{K}_{j}}}}\,)}$$
(10.3)
with
$$\overset{x}{\mathop{{{H}^{N}}}}\,=\frac{1}{2m}{{(\overset{\wedge }{\mathop{p}}\,-\frac{e}{c}A)}^{2}}-\sum\limits_{{{q}_{1}}=-N}^{N}{\sum\limits_{\alpha =1}^{M}{\frac{{{Z}_{\alpha }}}{|r-R_{\alpha }^{{{q}_{1}}}|}}=\frac{\overset{\wedge }{\mathop{p}}\,}{2m}+EN}$$
(10.4)
for a linear chain of 2N + 1 unit cells and M atoms in the cell, where the abbreviation EN denotes all the electron—nuclear interaction terms in the chain. In equation (10.3) summation over j indicates, as before, summation over all filled bands and integration in k-space over the first Brillouin zone.

Keywords

Dyson Equation Polymeric Crystal Crystal Orbital Longitudinal Elastic Modulus Longitudinal Acoustic Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • János J. Ladik
    • 1
  1. 1.University of Erlangen-NurembergErlangen-WaterlooFederal Republic of Germany

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