In condensed matter physics, the density of states (DOS) of a system describes the number of allowed modes or states per unit energy range. The density of states is defined as D ( E ) = N ( E ) / V , where N ( E ) δ δ E is the number of states in the system of volume V whose energies lie in the range from E to E + δ δ E . It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation.