Band structure

atoms - crystal - vacuum

In a single H-atom an electron resides in well known orbits. Note that the orbits are called s,p,d in order of increasing circular current.

Putting two atoms together leads to delocalized orbits across two atoms, a so called covalent bond. Due to Paulis principle in every state there is max one electron.

This can be continued with more atoms.

Using 6 carbon atoms one can create molecular orbits which allow for circular current. Filling the states following Pauli's principle leads to zero net current. Current due to uneven filling needs an energy investment.

Proceeding in a regular fashion and create a crystal, which may after creation be cut into a tape and fused together at the ends allow for circular currents.

For this regular solid the band structure can be calculated or measured.

Integrating over the k axis gives the bands of a semiconductor showing a full valence band and an empty conduction band. Generally stopping at the vacuum level is dumb, because some people want to calculate: photoemission, inverse photoemission, Semiconductor_detector#particle_detectors

After the band structure is determined states can be combined to generate wave packets. As this is analogous to wave packages in free space, the results are similar.

An alternative description, which does not really appreciate the strong Coulomb interaction, shoots free electrons into the crystal and looks at the scattering.

A third alternative description uses strongly localized unpaired electrons in chemical bonds, which looks almost like a Mott insulator.