Fermi–Dirac statistics

Fermi–Dirac statistics is a type of <a href="/facts/Quantum_statistics/hJaSBe1l">quantum statistics</a> that applies to the <a href="/facts/Physics/a7aH2y08">physics</a> of a <a href="/facts/Physical_system/tdSfxvIB">system</a> consisting of many non-interacting, <a href="/facts/Identical_particles/qg0mHeVR">identical particles</a> that obey the <a href="/facts/Pauli_exclusion_principle/lsBKGeHD">Pauli exclusion principle</a>. A result is the Fermi–Dirac distribution of particles over <a href="/facts/Energy_level/66x51Khc">energy states</a>. It is named after <a href="/facts/Enrico_Fermi/cmYcY15H">Enrico Fermi</a> and <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a>, each of whom derived the distribution independently in 1926. Fermi–Dirac statistics is a part of the field of <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a> and uses the principles of <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>.
Fermi–Dirac statistics applies to identical and indistinguishable particles with <a href="/facts/Half-integer/oJ29mf8G">half-integer</a> <a href="/facts/Spin_(physics)/4Jvp7e8P">spin</a> (1/2, 3/2, etc.), called <a href="/facts/Fermion/LEckdDsR">fermions</a>, in <a href="/facts/Thermodynamic_equilibrium/1D7nGm0d">thermodynamic equilibrium</a>. For the case of negligible interaction between particles, the system can be described in terms of single-particle <a href="/facts/Energy_eigenstates/HBQvbb6s">energy states</a>. A result is the Fermi–Dirac distribution of particles over these states where no two particles can occupy the same state, which has a considerable effect on the properties of the system. Fermi–Dirac statistics is most commonly applied to <a href="/facts/Electron/L0KBo5cW">electrons</a>, a type of fermion with <a href="/facts/Spin_1%2f2/3I929M4X">spin 1/2</a>.
A counterpart to Fermi–Dirac statistics is <a href="/facts/Bose%25E2%2580%2593Einstein_statistics/Utb2jN3n">Bose–Einstein statistics</a>, which applies to identical and indistinguishable particles with integer spin (0, 1, 2, etc.) called <a href="/facts/Bosons/XtPFcjb5">bosons</a>. In classical physics, <a href="/facts/Maxwell%25E2%2580%2593Boltzmann_statistics/l3Qf1Cxp">Maxwell–Boltzmann statistics</a> is used to describe particles that are identical and treated as distinguishable. For both Bose–Einstein and Maxwell–Boltzmann statistics, more than one particle can occupy the same state, unlike Fermi–Dirac statistics.

Fermi–Dirac statistics open-in-new

Fermi–Dirac statistics