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The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
For up to 10 −35 seconds after the Big Bang, the energy density of the universe was so high that the four forces of nature – strong, weak, electromagnetic, and gravitational – are thought to have been unified into one single force. The state of matter at this time is unknown.
The density of states function g(E) is defined as the number of electronic states per unit volume, per unit energy, for electron energies near E. The density of states function is important for calculations of effects based on band theory.
Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
Cubic equations of state are a specific class of thermodynamic models for modeling the pressure of a gas as a function of temperature and density and which can be rewritten as a cubic function of the molar volume.
Calculable is the ratio of the populations of the two states at room temperature (T ≈ 300 K) for an energy difference ΔE that corresponds to light of a frequency corresponding to visible light (ν ≈ 5 × 10 14 Hz). In this case ΔE = E 2 − E 1 ≈ 2.07 eV, and kT ≈ 0.026 eV.
The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is =, which means that its energy density decreases as =, where is a volume.In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.
As the density increases or the temperature decreases, the number of accessible states per particle becomes smaller, and at some point, more particles will be forced into a single state than the maximum allowed for that state by statistical weighting.