Symmetry Considerations

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


Many problems in solid state theory consist in solving the time-independent Schrödinger equation
$$H{\psi _n} = {E_n}{\psi _n}$$
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.



Irreducible Representation Brillouin Zone Point Group Factor Group Symmetry Operation 
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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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