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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.
An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions in a constant potential well. Fermions are elementary or composite particles with half-integer spin, thus follow Fermi–Dirac statistics. The equivalent model for integer spin particles is called the Bose gas (an ensemble of non ...
The thermodynamics of an ideal Bose gas is best calculated using the grand canonical ensemble.The grand potential for a Bose gas is given by: = = (). where each term in the sum corresponds to a particular single-particle energy level ε i; g i is the number of states with energy ε i; z is the absolute activity (or "fugacity"), which may also be expressed in terms of the chemical ...
In a semiconductor with an arbitrary density of states, i.e. a relation of the form = between the density of holes or electrons and the corresponding quasi Fermi level (or electrochemical potential) , the Einstein relation is [11] [12] =, where is the electrical mobility (see § Proof of the general case for a proof of this relation).
Effective mass (solid-state physics) In solid state physics, a particle's effective mass (often denoted ) is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement ...
Horse, horse tack. Venue. Indoor or outdoor riding arena. Barrel racing is a rodeo event in which a horse and rider attempt to run a cloverleaf pattern around preset barrels in the fastest time. In collegiate and professional ranks, it is usually a women's event, though both sexes compete at amateur and youth levels.
Statistical mechanics. Fermi–Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each ...
The results of the quantum harmonic oscillator can be used to look at the equilibrium situation for a quantum ideal gas in a harmonic trap, which is a harmonic potential containing a large number of particles that do not interact with each other except for instantaneous thermalizing collisions. This situation is of great practical importance ...