Independent electron approximation

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Independent electron approximation both 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 electrons 2. potential due to electron electron interaction is not periodic 3. 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 other 2.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.