Bloch wave

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A Bloch wave or Bloch state is the wavefunction of a particle (usually, an electron) placed in a periodic potential. It consists of the product of a plane wave and a periodic function, which has the same periodicity as the potential. The plane wave wavevector is unique only up to a reciprocal lattice vector, which gives rise to the concept of the Brillouin zone. For a given wavevector, there are a number of solutions to Schrodinger's equation for a Bloch electron. These solutions, called bands, have a finite energy spacing. The band structure is the collection of energy eigenstates within the first Brillouin zone. All the properties of electrons in a periodic potential can be calculated from this band structure, at least within the independent electron approximation.

It can be shown that a particle in a periodic potential must have this form by proving that translation operators commute with the Hamiltonian. This result is called Bloch's Theorem.

The concept of the Bloch state was developed by Felix Bloch in 1928.