Independent electron approximation
- Independent electron approximation
Independent electron approximationboth in the case of free electron theory and nearly-free electron approximation we use independent electron approximation. according to this we do not consider electron electron interaction in a crystal. the potential in a crystal is sum of potential due to ion-electron interactions and electron-electron interactions.
it is difficult to treat electron electron interaction when compared to ion-electron interactions because of the following reasons:
1. we are not aware of state functions of all the electrons2. potential due to electron electron interaction is not periodic3. we need to consider the dynamics of all the electrons at a time
we are able to use this approximation on the account of the fact that electron electron interaction is very weak when compared to ion-electron interactions because of the following reasons:
1.electrons with parallel spin stay away from each other2.even though they possess opposite spins they stay away from each other in order to have least energy for the system.
the only effect of electron electron interaction is that electrons distribute around the ions so that they screen the ions in the lattice from other electrons.
References
ELEMENTARY SOLID STATE PHYSICS-M.ALI OMAR, Pearson publishers
Wikimedia Foundation.
2010.
Look at other dictionaries:
Nearly-free electron model — Electronic structure methods Tight binding Nearly free electron model Hartree–Fock method Modern valence bond Generalized valence bond Møller–Plesset perturbat … Wikipedia
Electron configuration — Electron atomic and molecular orbitals Simp … Wikipedia
Electron diffraction — is a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern. This phenomenon occurs due to the wave particle duality, which states that a particle of matter (in this case the incident… … Wikipedia
Electron mobility — This article is about the mobility for electrons and holes in metals and semiconductors. For the general concept, see Electrical mobility. In solid state physics, the electron mobility characterizes how quickly an electron can move through a… … Wikipedia
Field electron emission — It is requested that a diagram or diagrams be included in this article to improve its quality. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. Field emission (FE) (also known as field… … Wikipedia
Born-Oppenheimer approximation — In quantum chemistry, the computation of the energy and wavefunction of an average size molecule is a formidable task that is alleviated by the Born Oppenheimer (BO) approximation. For instance the benzene molecule consists of 12 nuclei and 42… … Wikipedia
Free electron model — In three dimensions, the density of states of a gas of fermions is proportional to the square root of the kinetic energy of the particles. In solid state physics, the free electron model is a simple model for the behaviour of valence electrons in … Wikipedia
Bloch wave — A Bloch wave or Bloch state, named after Felix Bloch, is the wavefunction of a particle (usually, an electron) placed in a periodic potential. It consists of the product of a plane wave envelope function and a periodic function ( periodic Bloch… … Wikipedia
Electronic band structure — In solid state physics, the electronic band structure (or simply band structure) of a solid describes ranges of energy that an electron is forbidden or allowed to have. It is due to the diffraction of the quantum mechanical electron waves in the… … Wikipedia
Walsh diagram — of an HAH molecule. Walsh diagrams, often called angular coordinate diagrams or correlation diagrams, are representations of calculated orbital energies of a molecule versus a distortion coordinate, used for making quick predictions about the… … Wikipedia
