Energies of Electrons
In the simple band theory models, it is considered that electrons fill a continuum of levels, with two electrons in a level.
In reality electrons cannot have a continuum of energies, because certain energies are forbidden. At these energies, the electrons would be diffracted by the lattice.
The kinetic energy of a free electron particle is given by:
de Broglie's equation relates momentum and wavelength:
Combining with Bragg's Law, gives the forbidden energies:
or in k space: E= h2k2/(8mš2), where k = 2š/?