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Self energy (Read 1505 times)
Gerrit-Jan Linker
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Self energy
05.08.11 at 09:29:42
Self energy
The self-energy of a given charge distribution is the energy required to assemble the distribution by bringing in the constituent charges from infinity.  
In a condensed matter context relevant to electrons moving in a material, the self-energy represents the potential felt by the electron due to the surrounding medium's interactions with it.
The potential energy of two charges i and j is:  
Uij = qiqj/rij
or Uij = ρ(ri)driρj(rj)drj/rij
The total electrostatic energy UES is:
UES = ∑i,jUij = ∑Uij= ∫d3ri∫d3rjρ(ri)ρ(rj)/rij
We can partition the charge density in arbitrary pieces, e.g. in A and B:
UES = ∫Ad3riAd3riρ(ri)ρ(ri)/rii + ∫Bd3rjBd3rjρ(rj)ρ(rj)/rjj +
The first two terms are the self energies of A and B and the last term is the interaction energy between A and B.
Intermoleculaire wisselwerkingen, Piet van Duijnen, 1993
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« Last Edit: 05.08.11 at 09:40:25 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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