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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 that are available to be occupied. Unlike isolated systems, like atoms or molecules in 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. ==Introduction== 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 allows 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, and therefore at this associated energy, while no states are available at other energy levels: 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 or the wave vector, the system-specific energy dispersion relation between ''E'' and ''k'' must be known. For example, the density of states for electrons in a semiconductor is shown in red in Fig. 4 (in section 5). For electrons at the conduction band edge, very few states are available for the electron to occupy. As the electron increases in energy, the electron density of states increases and more states become available for occupation. However, because there are no states available for electrons to occupy within the bandgap, electrons at the conduction band edge must lose at least of energy in order to transition to another available mode. In general, the topological properties of the system have a major impact on the properties of the density of states. The most well-known systems, like neutronium in neutron stars and free electron gases in metals (examples of degenerate matter and a Fermi gas), have a 3-dimensional Euclidean topology. Less familiar systems, like 2-dimensional electron gases (2DEG) in graphite layers and the Quantum Hall effect system in MOSFET type devices, have a 2-dimensional Euclidean topology. Even less familiar are Carbon nanotubes, the quantum wire and Luttinger liquid with their 1-dimensional topologies. Systems with 1D and 2D topologies are likely to become more common, assuming developments in nanotechnology and materials science proceed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Density of states」の詳細全文を読む スポンサード リンク
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