Voltage & Its Effect on Material Energy Levels

[hokhani]

If we apply a voltage V to a portion of material, does this voltage only shift the energy levels of that portion, as much as V, or it makes an electric field inside that portion which changes the levels in a different manner according to a new Hamiltonian?

 

[AURUM]

if we do apply a voltage across a material it sets up an electric field inside it but i don't know what do you mean by Hamiltonian.sorry for incomplete answer.