Magnetic, Electric, and Mechanical Properties of Polymers

  • János J. Ladik


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
$$\overset{x}{\mathop{H}}\,=\frac{\overset{\wedge }{\mathop{p}}\,}{2m}+V(r)$$
$$\overset{\wedge }{\mathop{p}}\,=\overset{\wedge }{\mathop{p}}\,-\frac{e}{c}A;\,H(r)=curlA(r)$$
In the Hartree-Fock case one can then write
$$\overset{\wedge }{\mathop{F}}\,=\overset{x}{\mathop{{{H}^{N}}}}\,+\sum\limits_{j}{(2\overset{\wedge }{\mathop{{{J}_{j}}}}\,-\overset{\wedge }{\mathop{{{K}_{j}}}}\,)}$$
$$\overset{x}{\mathop{{{H}^{N}}}}\,=\frac{1}{2m}{{(\overset{\wedge }{\mathop{p}}\,-\frac{e}{c}A)}^{2}}-\sum\limits_{{{q}_{1}}=-N}^{N}{\sum\limits_{\alpha =1}^{M}{\frac{{{Z}_{\alpha }}}{|r-R_{\alpha }^{{{q}_{1}}}|}}=\frac{\overset{\wedge }{\mathop{p}}\,}{2m}+EN}$$
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.


Dyson Equation Polymeric Crystal Crystal Orbital Longitudinal Elastic Modulus Longitudinal Acoustic Mode 
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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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