A Bloch wave or Bloch state, named after Felix Bloch, is the wavefunction of a particle placed in a periodic potential. It consists of the product of a plane wave envelope function and a periodic function which has the same periodicity as the potential. The result that the eigenfunctions can be written in this form for a periodic system is called Bloch's theorem. The corresponding energy eigenvalue is (k)= ( k + K), periodic with periodicity K of a reciprocal lattice vector. Because the energies associated with the index n vary continuously with wavevector k we speak of an energy band with band index n. Because the eigenvalues for given n are periodic in k, all distinct values of (k) occur for k-values within the first Brillouin zone of the reciprocal lattice.

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