Bloch's Theorem is one of the foundations of solid-state physics
. It states the following:
Given a periodic potential
), the solutions to the time-independent Schrödinger equation
are of the form
Ψ(r) = eikru(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.