Wannier function

Named after the Swiss physicist Gregory Hugh Wannier Wannier representation is a term used in solid state physics. In the tight-binding approximation, a description of the electronic wave functions in the lattice- periodic Bloch- base is no longer meaningful. Rather, we construct the state function of atomic wave functions. But these are not orthonormal. However, you can construct an orthonormal basis of localized states from the Bloch functions.

It is a Bloch function and the associated Wannier state. The reverse design of the Bloch states of the Wannier states is then called

The larger the lattice constant, the stronger the Wannierzustände are located. They are more closely related to the atomic states. But instead of the Wannier state simply equate an atomic state, approaching him by a linear combination of atomic states ( LCAO ):

The set U represents represents a subspace of the atomic states