Density of states

In solid-state and condensed matter physics, the density of states (DOS) of a system describes the number of states per interval of energy at each energy level available to be occupied. Unlike isolated systems, like atoms or molecules in the gas phase, the density distributions are not discrete like a spectral density but continuous. A high DOS at a specific energy level means that there are many states available for occupation. A DOS of zero means that no states can be occupied at that energy level. In general a DOS is an average over the space and time domains occupied by the system. Local variations, most often due to distortions of the original system, are often called local density of states (LDOS). If the DOS of an undisturbed system is zero, the LDOS can locally be non-zero due to the presence of a local potential.

In quantum mechanical (QM) systems, waves, or wave-like particles can occupy modes or states with wavelengths and propagation directions dictated by the system. Often 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. Depending on the QM system the density of states can be calculated for electrons, photons, or phonons, and can be given as a function of either energy or the wave vector k. The DOS is usually represented by one of the symbols g, ρ, D, n, or N. To convert between the DOS as a function of the energy and the DOS as a function of the wave vector, the system-specific energy dispersion relation between E and k must be known.

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