Waves or wave-like particles can occupy stateswith wavelengths and propagation directions. Only specific states are permitted. In some systems, the interatomic spacing and the atomic charge of the material allow only electrons of certain wavelengths to exist. In other systems, the crystalline structure of the material allows waves to propagate in one direction, while suppressing wave propagation in another direction. Thus it can happen that many states are possible at a specific wavelength, while no states are available at other energy levels of the associated energy: this distribution is characterized by the density of states (DOS or D(E)).