In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one...

particles: any physical prediction relating multiple indistinguishable particles must not change when the particles are exchanged. [citation needed] In a quantum...

states space of a variable or unknown number of identical particles from a single particle Hilbert space H. It is named after V. A. Fock who first introduced...

Look up indistinguishability in Wiktionary, the free dictionary. Indistinguishability may refer to: Identical (indistinguishable) particles Computational...

non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It...

example, a system with two indistinguishable particles, with particle 1 in state ⁠ ψ 1 {\displaystyle \psi _{1}} ⁠ and particle 2 in state ⁠ ψ 2 {\displaystyle...

material particles over various energy states in thermal equilibrium. It is applicable when the temperature is high enough or the particle density is...

when one of its particles is replaced by another particle, these two particles are called distinguishable. Bosons Bosons are particles with integer spin...

interaction is a quantum mechanical constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of...

indistinguishable particles (in fact, indistinguishability is a prerequisite for defining a chemical potential in a consistent manner; all particles of...

non-interacting identical particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state...

parameters of separate particles. When an ensemble describes a system of particles with similar properties, their number is called the particle number and usually...

where m is the number of sets of indistinguishable particles in the final state, and kj is the number of particles of type j, so that ∑ j = 1 m k j =...

Bose–Einstein correlation between particles and antiparticles[citation needed]. The wave function of two identical particles is symmetric or antisymmetric...

1899 to 1935. He is known for first proposing the concept of indistinguishable particles leading to quantum statistics. He came from a Jewish family of...

derivation of entropy that does not take into account the indistinguishability of particles yields an expression for entropy which is not extensive (is...

average particle number are fixed. In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that...

fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson that couples to (interacts with) particles whose mass...

hypothesized microscopic particles in particle physics, condensed matter physics and cosmology. Elementary particles are particles with no measurable internal...

gas as composed of numerous particles, too small to be seen with a microscope, in constant, random motion. These particles are now known to be the atoms...

helium-4 (the alpha particle), carbon-12, lead-208, and many others. As quantum particles, the behaviour of multiple indistinguishable bosons at high densities...

denotes factorial. The "correction" in the denominator account for indistinguishable particles in the same condition. Boltzmann could also be considered one...

of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with...

of particles, where any two particles of the same kind are indistinguishable and exchangeable. When the state is written in terms of the particles' individual...

S is the entropy, μ is the chemical potential, and N is the number of particles in the system. The change in the grand potential is given by d Φ G = d...

a gas of indistinguishable particles. Einstein noted that Bose's statistics applied to some atoms as well as to the proposed light particles, and submitted...

} ( 2 π {\displaystyle 2\pi } ) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of π {\displaystyle...

for various types of particle. The grand canonical ensemble contains states of varying energy and varying numbers of particles; the different states...

The particles predicted by parastatistics have not been experimentally observed. Consider the operator algebra of a system of N identical particles. This...

particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. If a given particle is...