A
Bloch wave (also called
Bloch state or
Bloch function or
Bloch wave function), named after Swiss
physicist Felix Bloch, is a type of
wavefunction for a particle in a periodically-repeating environment, most commonly an
electron in a
crystal. A wavefunction ψ is a Bloch wave if it has the form:
where
r is position, ψ is the Bloch wave,
u is a
periodic function with the same periodicity as the crystal,
k is a vector of real numbers called the
crystal wave vector,
e is
Euler's number, and
i is the
imaginary unit. In other words, if you multiply a
plane wave by a periodic function, you get a Bloch wave.