Bonding Forces and Energy Bands in Solids

• Electrons are controlled to sets of discrete energy levels in atoms, with large gaps among them in which no energy state is obtainable for the electron to occupy.
• Electrons in solids as well are restricted to certain energies and are not permitted at other energies.
• Variation → in the solid, the electron has a range (or band) of available energies.
• The discrete energy levels of the isolated atom spread into bands of energies in the solid since

1. In the solid, the wave functions of electrons in neighboring atoms overlap, so it influences the potential energy term and the boundary conditions in the Schrödinger equation, and different energies are acquired in the solution, and
2. An electron is not essentially localized at a specific atom.

• The affect of neighboring atoms on the energy levels of a specific atom can be treated as a small perturbation, giving rise to shifting and splitting of energy states into energy bands.