Editing Superlattice (section)

== Wannier functions ==

By definition the [[Bloch's theorem|Bloch functions]] are delocalized over the whole superlattice. This may provide difficulties if electric fields are applied or effects due to the superlattice's finite length are considered. Therefore, it is often helpful to use different sets of basis states that are better localized. A tempting choice would be the use of eigenstates of single quantum wells. Nevertheless, such a choice has a severe shortcoming: the corresponding states are solutions of two different [[Hamiltonian (quantum mechanics)|Hamiltonian]]s, each neglecting the presence of the other well. Thus these states are not orthogonal, creating complications. Typically, the coupling is estimated by the transfer Hamiltonian within this approach. For these reasons, it is more convenient to use the set of [[Wannier function]]s.