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Symmetry Considerations

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Part of the Physics and Chemistry of Materials with Layered Structures book series (PCMA, volume 3)

Abstract

Many problems in solid state theory consist in solving the time-independent Schrödinger equation
$$H{\psi _n} = {E_n}{\psi _n}$$
(A1)
to obtain the energy eigenvalues E n together with the corresponding eigenfunctions ψ n . Since one is dealing with a large number of particles (~1023 electrons + nuclei) a solution of this many-particle problem can only be obtained after various approximations and simplifications. Without going into detail we shall simply mention the usual approximations made in solving Schrödinger’s equation:
  1. (i)

    Since our main interest is in the electronic system, we separate the motion of electrons and nuclei and consider the latter as being fixed (Born-Oppenheimer approximation). This approximation of course is invalid if we are interested in finite temperature effects. It is, however, in most cases sufficient to treat finite temperature effects, like electron-phonon coupling by perturbation.

     
  2. (ii)

    The remaining many-electron problem can be reduced to a one-electron problem by defining an averaged potential, like the Hartree or Hartree-Fock potential. Exchange and correlation can be treated in several local or non-local approximations according to their importance in the particular problem. The resulting one-electron potential can be iterated in a self-consistent way until convergence is reached.

     
  3. (iii)

    Spin and other relativistic effects are usually introduced through the standard two-component Pauli matrix formalism. This approximation of Dirac’s treatment is valid in the low energy region we are concerned with.

     

Keywords

Irreducible Representation Brillouin Zone Point Group Factor Group Symmetry Operation 
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

© D. Reidel Publishing Company, Dordrecht, Holland 1979

Authors and Affiliations

  1. 1.Bell LaboratoriesMurray HillUSA

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