Concept in quantum mechanics of perfectly substitutable particles
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Statistical mechanics
Thermodynamics
Kinetic theory
Particle statistics
Spin–statistics theorem
Indistinguishable particles
Maxwell–Boltzmann
Bose–Einstein
Fermi–Dirac
Parastatistics
Anyonic statistics
Braid statistics
Thermodynamic ensembles
NVE Microcanonical
NVT Canonical
µVT Grand canonical
NPH Isoenthalpic–isobaric
NPT Isothermal–isobaric
Models
Debye
Einstein
Ising
Potts
Potentials
Internal energy
Enthalpy
Helmholtz free energy
Gibbs free energy
Grand potential / Landau free energy
Scientists
Maxwell
Boltzmann
Bose
Gibbs
Einstein
Ehrenfest
von Neumann
Tolman
Debye
Fermi
v
t
e
In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules. Quasiparticles also behave in this way. Although all known indistinguishable particles only exist at the quantum scale, there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability, as explored in quantum statistics. They were first discussed by Werner Heisenberg and Paul Dirac in 1926.[1]
There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which cannot (as described by the Pauli exclusion principle). Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei.
The fact that particles can be identical has important consequences in statistical mechanics, where calculations rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.
^Gottfried, Kurt (2011). "P. A. M. Dirac and the discovery of quantum mechanics". American Journal of Physics. 79 (3): 2, 10. arXiv:1006.4610. doi:10.1119/1.3536639. S2CID 18229595.
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indistinguishableparticles (in fact, indistinguishability is a prerequisite for defining a chemical potential in a consistent manner; all particles of...
example, a system with two indistinguishableparticles, with particle 1 in state ψ 1 {\displaystyle \psi _{1}} and particle 2 in state ψ 2 {\displaystyle...
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the number of sets of indistinguishableparticles in the final state, and k j {\displaystyle k_{j}\,} is the number of particles of type j, so that ∑ j...
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derivation of entropy that does not take into account the indistinguishability of particles yields an expression for entropy which is not extensive (is...
degrees of freedom. In a system of particles, the number of degrees of freedom n depends on the number of particles N in a way that depends on the physical...
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interchange of identical particles. That is, it would be neither a boson nor a fermion, but subject to a braid statistics. Such particles have been discussed...
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physical manifestation for the mode with the larger wavenumber is indistinguishable from the one with the smaller wavenumber. Therefore, the study of...
long as the particles are distinguishable, a point in phase space is said to be a microstate of the system. (For indistinguishableparticles a microstate...
{\displaystyle N!} has been included to account for the indistinguishability of particles (see Gibbs paradox). In the large N {\displaystyle N} limit...
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