Bloch wave

A Bloch wave or Bloch state, named after Felix Bloch, is the wavefunction of a particle (usually, an periodic potential. It consists of the product of a plane wave envelope function and a periodic function (periodic Bloch function) $\, u_{nk}(r)$ which has the same periodicity as the potential:

$\psi_{n\mathbf{k}}(\mathbf{r})=e^{i\mathbf{k}\cdot\mathbf{r}}u_{n\mathbf{k}}(\mathbf{r}).$