What is pseudopotential, core electrons, solid structure, method

Pseudopotential:

The property of the solids depend upon the electrons in valence-conduction bands and these electrons which move in the solid are found outside the atomic core. Thus we should concerned about the description of the wave function outside the atomic core. Hence, the pseudo-potential is  one which gives rise to essentially the same wave function outside the atomic core as the original atomic potential.

Pseudo-potential concept is to replace the atomic potentials by a weak potential which gives rise to the same scattering amplitude for the conduction electrons.