Editing Superlattice (section)

== Wannier–Stark ladder ==

Applying an electric field ''F''  to the superlattice structure causes the Hamiltonian to exhibit an additional scalar potential ''eφ''(''z'') = −''eFz'' that destroys the translational invariance. In this case, given an eigenstate with wavefunction <math> \Phi_0 (z) </math> and energy <math>E_0</math>, then the set of states corresponding to wavefunctions <math>\Phi_j (z)= \Phi_0 (z-jd) </math> are eigenstates of the Hamiltonian with energies ''E''<sub>''j''</sub> = ''E''<sub>0</sub> − ''jeFd''. These states are equally spaced both in energy and real space and form the so-called ''Wannier–Stark ladder''. The potential <math> \Phi_0 (z)</math> is not bounded for the infinite crystal, which implies a continuous energy spectrum. Nevertheless, the characteristic energy spectrum of these Wannier–Stark ladders could be resolved experimentally.