Pauli exclusion principle

Pauli principleexclusion principlePauli's exclusion principlePauli exclusionexclusion rulefermionic degeneracy pressurePauli exclusive principlePauli repulsionPrincipletwo bodies cannot occupy the same space at the same time
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.wikipedia
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Fermion

fermionsFermionichalf-integer spin
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
These particles obey the Pauli exclusion principle.

Wolfgang Pauli

Pauli Wolfgang Pauli’sPauli, Wolfgang
This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.
In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or Pauli principle".

Electron

electronse − electron mass
In the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number,, the azimuthal quantum number, m, the magnetic quantum number, and m s, the spin quantum number. Fermions include elementary particles such as quarks, electrons and neutrinos.
Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle.

Spin (physics)

spinnuclear spinspins
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
When combined with the spin-statistics theorem, the spin of electrons results in the Pauli exclusion principle, which in turn underlies the periodic table of chemical elements.

Identical particles

indistinguishabilityidenticalindistinguishable
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. A more rigorous statement is that concerning the exchange of two identical particles the total wave function is antisymmetric for fermions, and symmetric for bosons.
There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which do not share quantum states as described by the Pauli exclusion principle.

Spin–statistics theorem

spin-statistics theoremSpin Statistics TheoremBecause mesons are bosons
This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.
This is the Pauli exclusion principle: two identical fermions cannot occupy the same state.

Atomic orbital

orbitalatomic orbitalselectron cloud
For example, if two electrons reside in the same orbital, then their n,, and m values are the same, therefore their m s must be different, and thus the electrons must have opposite half-integer spin projections of 1/2 and −1/2.
Nevertheless, one has to keep in mind that electrons are fermions ruled by the Pauli exclusion principle and cannot be distinguished from the other electrons in the atom.

Quark

quarksantiquarkantiquarks
Fermions include elementary particles such as quarks, electrons and neutrinos.
They are subject to the Pauli exclusion principle, which states that no two identical fermions can simultaneously occupy the same quantum state.

Fermi–Dirac statistics

Fermi–Dirac distributionFermi–DiracFermi-Dirac distribution
(Fermions take their name from the Fermi–Dirac statistical distribution that they obey, and bosons from their Bose–Einstein distribution.)
In quantum statistics, a branch of physics, Fermi–Dirac statistics describe a distribution of particles over energy states in systems consisting of many identical particles that obey the "Pauli exclusion principle".

Quantum number

quantum numbersq-number3d, 4d, and 5d
In the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number,, the azimuthal quantum number, m, the magnetic quantum number, and m s, the spin quantum number.
Each electron in any individual orbital must have different quantum numbers because of the Pauli exclusion principle, therefore an orbital never contains more than two electrons.

Baryon

baryonic matterbaryonsbaryonic
Additionally, baryons such as protons and neutrons (subatomic particles composed from three quarks) and some atoms (such as helium-3) are fermions, and are therefore described by the Pauli exclusion principle as well.
Baryons are strongly interacting fermions; that is, they are acted on by the strong nuclear force and are described by Fermi–Dirac statistics, which apply to all particles obeying the Pauli exclusion principle.

Bose–Einstein statistics

Bose–Einstein distributionBose–EinsteinBose
(Fermions take their name from the Fermi–Dirac statistical distribution that they obey, and bosons from their Bose–Einstein distribution.)
The Bose–Einstein statistics apply only to those particles not limited to single occupancy of the same state—that is, particles that do not obey the Pauli exclusion principle restrictions.

Principal quantum number

nprincipal1
In the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number,, the azimuthal quantum number, m, the magnetic quantum number, and m s, the spin quantum number. He found an essential clue in a 1924 paper by Edmund C. Stoner, which pointed out that, for a given value of the principal quantum number (n), the number of energy levels of a single electron in the alkali metal spectra in an external magnetic field, where all degenerate energy levels are separated, is equal to the number of electrons in the closed shell of the noble gases for the same value of n.
Two electrons belonging to the same atom cannot have the same values for all four quantum numbers, due to the Pauli exclusion principle.

Boson

bosonsBosonicinteger spin
Particles with an integer spin, or bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser or atoms in a Bose–Einstein condensate.
Two or more identical fermions cannot occupy the same quantum state (see Pauli exclusion principle), and they are sometimes said to be the constituents of ordinary "rigid" matter.

Photon

photonslight quantaincident photon
Bosons include the photon, the Cooper pairs which are responsible for superconductivity, and the W and Z bosons.
Also, the photon does not obey the Pauli exclusion principle, but instead obeys Bose–Einstein statistics.

Atom

atomsatomic structureatomic
Additionally, baryons such as protons and neutrons (subatomic particles composed from three quarks) and some atoms (such as helium-3) are fermions, and are therefore described by the Pauli exclusion principle as well. One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations.
Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time.

Neutron

neutronsfree neutronn
Additionally, baryons such as protons and neutrons (subatomic particles composed from three quarks) and some atoms (such as helium-3) are fermions, and are therefore described by the Pauli exclusion principle as well.
The Pauli exclusion principle therefore disallows the decay of a neutron to a proton within stable nuclei.

Wave function

wavefunctionwave functionsnormalized
A more rigorous statement is that concerning the exchange of two identical particles the total wave function is antisymmetric for fermions, and symmetric for bosons.
The antisymmetry feature of fermionic wave functions leads to the Pauli principle.

Elementary particle

elementary particlesparticleparticles
Fermions include elementary particles such as quarks, electrons and neutrinos.
Bosons differ from fermions in the fact that multiple bosons can occupy the same quantum state (Pauli exclusion principle).

Bose–Einstein condensate

Bose–Einstein condensationBose-Einstein condensateBose-Einstein condensation
Particles with an integer spin, or bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser or atoms in a Bose–Einstein condensate.
Cooling fermions to extremely low temperatures has created degenerate gases, subject to the Pauli exclusion principle.

Edmund Clifton Stoner

E. C. StonerEdmund C. StonerStoner
He found an essential clue in a 1924 paper by Edmund C. Stoner, which pointed out that, for a given value of the principal quantum number (n), the number of energy levels of a single electron in the alkali metal spectra in an external magnetic field, where all degenerate energy levels are separated, is equal to the number of electrons in the closed shell of the noble gases for the same value of n.
After graduation, he worked at the Cavendish Laboratory on the absorption of X-rays by matter and electron energy levels; his 1924 paper on this subject prefigured the Pauli exclusion principle.

Niels Bohr

BohrNiels Henrik David BohrBohr, Niels
In 1922, Niels Bohr updated his model of the atom by assuming that certain numbers of electrons (for example 2, 8 and 18) corresponded to stable "closed shells".
An important development came in 1924 with Wolfgang Pauli's discovery of the Pauli exclusion principle, which put Bohr's models on a firm theoretical footing.

Electron configuration

electronic configurationconfigurationelectronic structure
One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations.
The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics, in particular the Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four quantum numbers.

Half-integer

half-integershalf-integralhalves of odd integers
"Half-integer spin" means that the intrinsic angular momentum value of fermions is (reduced Planck's constant) times a half-integer (1/2, 3/2, 5/2, etc.).
In physics, the Pauli exclusion principle results from definition of fermions as particles which have spins that are half-integers.

Electronic band structure

band structureband theoryenergy band
In conductors and semiconductors, there are very large numbers of molecular orbitals which effectively form a continuous band structure of energy levels.
The Pauli exclusion principle dictates that no two electrons can have the same quantum numbers in a molecule.