# Symmetry Considerations

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## Abstract

*E*

_{ n }together with the corresponding eigenfunctions

*ψ*

_{ n }. Since one is dealing with a large number of particles (~10

^{23}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:

- (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.

- (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.

- (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## Preview

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