Under the field, some will adjust their state slightly, adopting a different wave vector.
Under a field electrons are not able to adopt a different wave vector because there are no empty states to move into.
When this happens, we have three frequencies which all share the same wave vector, and are thus resonant with the cavity.
In multidimensional systems, the wavenumber is also the magnitude of the wave vector.
Here is the magnitude of the wave vector of the laser.
The magnitude of the wave vector is related to the energy as:
Band structure describes the relationship between energy(E) and wave vector(k).
In the context of special relativity the wave vector can also be defined as a four-vector.
The set of all such wave vectors defines the first Brillouin zone.
Each expansion corresponds to a projection of the wave vector onto a basis.