Bloch's Theorem is one of the foundations of

solid-state physics. It states the following:

Given a

periodic potential V(

**r**), the solutions to the

time-independent Schrödinger equation are of the form

Ψ(**r**) = e^{ikr}u(**r**),

where u(**r**) has the same periodicity as V(**r**).

Since the position of atoms in perfect crystals is periodic (neglecting thermal vibrations--see phonon), the potential in a crystal is periodic as well. Therefore the electron wavefunctions in a crystal obey Bloch's Theorem and are sometimes called Bloch functions. The vectors **k**, called Bloch wavevectors, are of great importance. The vectors **k** are said to belong to the reciprocal lattice space, or k-space of a crystal.