I How Is the Ion Lattice Approximation Justified in Electron Dynamics?

[aaaa202]

To solve the full many-body electron problem one often uses the approximation that the dynamics of the electron system, is that of N interacting electrons living in a periodic lattice of positive ion cores. What justifies this approximation and does it have a particular name?

 

[DrDu]

The approximation is here that the nuclei are assumed to be located at their equilibrium position. This is called the "crude adiabatic approximation". The "adiabatic approximation" (not the crude one) would solve the electronic problem for the momentaneous position of the nuclei.

 

[aaaa202]

okay is it related to the Born-Oppenheimer approximation?

 

[DrDu]

Basically yes. This is discussed in the book by huang and born dynamical theory of crystal lattices which is also online