- Pauli exclusion principle
The

**Pauli exclusion principle**is a quantum mechanical principle formulated byWolfgang Pauli in 1925. It states that no two identicalfermions may occupy the samequantum state "simultaneously". A more rigorous statement of this principle is that, for two identical fermions, the total wave function is anti-symmetric. For electrons in a single atom, it states that no two electrons can have the same four quantum numbers, that is, if "n", "l", and "m_{l}" are the same, "m_{s}" must be different such that the electrons have opposite spins.In relativistic

quantum field theory , the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin. It does not follow from any spin relation in nonrelativistic quantum mechanics.**Overview**The Pauli exclusion principle is one of the most important principles in

physics , primarily because the three types of particles from which ordinarymatter is made—electron s,proton s, andneutron s—are all subject to it; consequently, all material particles exhibit space-occupying behavior. The Pauli exclusion principle underpins many of the characteristic properties of matter from the large-scale stability of matter to the existence of the periodic table of the elements.Particles with antisymmetric wave functions are called

fermion s—and obey the Pauli exclusion principle. Apart from the familiar electron, proton and neutron, these includeneutrino s andquark s (from which protons and neutrons are made), as well as someatom s likehelium-3 . All fermions possess "half-integer spin", meaning that they possess an intrinsicangular momentum whose value is $hbar\; =\; h/2pi$ (Planck's constant divided by 2π) times ahalf-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics, fermions are described by "antisymmetric states", which are explained in greater detail in the article onidentical particles .Particles with integer spin have a symmetric wave function and are called

boson s; in contrast to fermions, they may share the same quantum states. Examples of bosons include thephoton and theW and Z bosons .**History**In the early 20th century, it became evident that atoms and molecules with pairs of electrons or even numbers of electrons are more stable than those with odd numbers of electrons. In the famous 1916 article " [

*http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Lewis-1916/Lewis-1916.html The Atom and the Molecule*] " byGilbert N. Lewis , for example, rule three of his six postulates of chemical behavior states that the atom tends to hold an even number of electrons in the shell and especially to hold eight electrons which are normally arranged symmetrically at the eight corners of a cube (see:cubical atom ). In 1919, the American chemistIrving Langmuir suggested that theperiodic table could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set ofelectron shell s about the nucleus. [*cite journal*] In 1922,

last=Langmuir | first=Irving

title=The Arrangement of Electrons in Atoms and Molecules

journal=Journal of the American Chemical Society

year=1919 | volume=41 | issue=6 | pages=868–934

url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Langmuir-1919b.html

accessdate=2008-09-01Niels 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".Pauli looked for an explanation for these numbers which were at first only empirical.At the same time he was trying to explain experimental results in the

Zeeman effect in atomic spectroscopy and inferromagnetism . He found an essential clue in a 1924 paper by E.C.Stoner which pointed out that for a given value of theprincipal quantum number (n), the number of energy levels of a single electron in thealkali metal spectra in an external magnetic field, where alldegenerate energy level s are separated, is equal to the number of electrons in the closed shell of therare gas es for the same value of n. This led Pauli to realize that the complicated numbers of electrons in closed shells can be reduced to the simple rule "one" per state, if the electron states are defined using four quantum numbers. For this purpose he introduced a new two-valued quantum number, identified bySamuel Goudsmit andGeorge Uhlenbeck aselectron spin .**Connection to quantum state symmetry**The Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to the assumption that the wavefunction is antisymmetric. An antisymmetric two-particle state is represented as a sum of states in which one particle is in state $scriptstyle\; |x\; angle$ and the other in state $scriptstyle\; |y\; angle$::$$

psi angle = sum_{xy} A(x,y) |x,y angleand antisymmetry under exchange means that A(x,y) = -A(y,x). This implies that A(x,x)=0, which is Pauli exclusion. It is true in any basis, since unitary changes of basis keep antisymmetric matrices antisymmetric, although strictly speaking, the quantity A(x,y) is not a matrix but an antisymmetric rank two tensor.

Conversely, if the diagonal quantities A(x,x) are zero "in every basis", then the wavefunction component::$A(x,y)=langle\; psi|x,y\; angle\; =\; langle\; psi\; |\; (\; |x\; angle\; otimes\; |y\; angle\; )$

is necessarily antisymmetric. To prove it, consider the matrix element::$|\; ((|x\; angle\; +\; |y\; angle)otimes(|x\; angle)),\; math>$

This is zero, because the two particles have zero probability to both be in the superposition state $scriptstyle\; |x\; angle\; +\; |y\; angle$. But this is equal to:$langle\; psi\; |x,x\; angle\; +\; langle\; psi\; |x,y\; angle\; +\; langle\; psi\; |y,x\; angle\; +\; langle\; psi\; |\; y,y\; angle,$

The first and last terms on the right hand side are diagonal elements and are zero, and the whole sum is equal to zero. So the wavefunction matrix elements obey:

:$langle\; psi|x,y\; angle\; +\; langlepsi\; |y,x\; angle\; =\; 0,$.

or:$A(x,y)=-A(y,x),$

According to the

spin-statistics theorem , particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.**Consequences****Atoms and the Pauli principle**The Pauli exclusion principle helps explain a wide variety of physical phenomena. One such consequence of the principle is the elaborate

electron shell structure ofatom s and of the way atoms share electron(s) - thus variety of chemical elements and of their combinations (chemistry). (An electrically neutral atom contains boundelectron s equal in number to the protons in the nucleus. Since electrons are fermions, the Pauli exclusion principle forbids them from occupying the same quantum state, so electrons have to "pile on top of each other" within an atom).For example, consider a neutral

helium atom, which has two bound electrons. Both of these electrons can occupy the lowest-energy ("1s") states by acquiring opposite spin. This does not violate the Pauli principle because spin is part of the quantum state of the electron, so the two electrons are occupying different quantum states. However, the spin can take only two different values (oreigenvalue s). In alithium atom, which contains three bound electrons, the third electron cannot fit into a "1s" state, and has to occupy one of the higher-energy "2s" states instead. Similarly, successive elements produce successively higher-energy shells. The chemical properties of an element largely depend on the number of electrons in the outermost shell, which gives rise to the periodic table of the elements.**olid state properties and the Pauli principle**In conductors and

semi-conductor sfree electron s have to share entire bulk space - thus their energy levels stack up creatingband structure out of each atomicenergy level . In strong conductors (metal s) electrons are so degenerate that they can not even contribute much intothermal capacity of a metal. Many mechanical, electrical, magnetic, optical and chemical properties of solids are the direct consequence of Pauli exclusion.**tability of matter**It has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume. The history of the demonstration of this fact is outlined in " [

*http://se02.xif.com/pages/sn_edpik/ps_3.htm The Stability of Matter, Science News Online, 14 October 1995*] ". The first suggestion in 1931 was byPaul Ehrenfest , who pointed out that the electrons of each atom cannot all fall into the lowest-energy orbital and must occupy successively larger shells. Atoms therefore occupy a volume and cannot be squeezed too close together.A more rigorous proof was provided by

Freeman Dyson and Andrew Lenard in 1967, who considered the balance of attractive (electron-nuclear) and repulsive (electron-electron and nuclear-nuclear) forces and showed that ordinary matter would collapse and occupy a much smaller volume without the Pauli principle. The consequence of the Pauli principle here is that electrons of the same spin are kept apart by a repulsiveexchange force orexchange interaction . This is a short-range force which is additional to the long-range electrostatic orcoulombic force . This additional force is therefore responsible for the everyday observation in the macroscopic world that two solid objects cannot be in the same place in the same time.Dyson and Lenard did not consider the extreme magnetic or gravitational forces which occur in some astronomical objects. In 1995

Elliott Lieb and coworkers showed that the Pauli principle still leads to stability in intense magnetic fields as inneutron stars , although at much higher density than in ordinary matter. In sufficiently intense gravitational fields, matter does collapse to form ablack hole .**Astrophysics and the Pauli principle**Astronomy provides another spectacular demonstration of this effect, in the form of white dwarf stars and

neutron star s. For both such bodies, their usual atomic structure is disrupted by large gravitational forces, leaving the constituents supported by "degeneracy pressure" alone. This exotic form of matter is known asdegenerate matter . In white dwarfs, the atoms are held apart by theelectron degeneracy pressure . In neutron stars, which exhibit even larger gravitational forces, the electrons have merged with theproton s to formneutron s, which produce a larger degeneracy pressure. Neutrons are the most "rigid" objects known - theirYoung modulus (or more accurately,bulk modulus ) is 20 orders of magnitude larger than that of diamond.**See also***

Exchange force

*Exchange interaction

*Exchange symmetry

*Hund's rule **References***cite book | author=Dill, Dan | title=Notes on General Chemistry (2nd ed.) | chapter = Chapter 3.5, Many-electron atoms: Fermi holes and Fermi heaps | publisher=W. H. Freeman | year=2006 | id=ISBN 1-4292-0068-5

*cite book | author=Griffiths, David J.|title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |id=ISBN 0-13-805326-X

*cite book | author=Liboff, Richard L. | title=Introductory Quantum Mechanics | publisher=Addison-Wesley | year=2002 | id=ISBN 0-8053-8714-5

*cite book | author=Massimi, Michela | title=Pauli's Exclusion Principle | publisher=Cambridge University Press | year=2005 | id=ISBN 0-521-83911-4

*cite book | author=Tipler, Paul; Llewellyn, Ralph | title=Modern Physics (4th ed.) | publisher=W. H. Freeman | year=2002 | id=ISBN 0-7167-4345-0**External links*** [

*http://nobelprize.org/nobel_prizes/physics/laureates/1945/pauli-lecture.html Nobel Lecture: Exclusion Principle and Quantum Mechanics*] Pauli's own account of the development of the Exclusion Principle.

* [*http://www.energyscience.org.uk/essays/ese06.htm The Exclusion Principle*] (1997), Pauli's exclusion rules vs. the Aspden exclusion rules (plus the radiation factor, Larmor radiation formula, elliptical motion, the quantum states, occupancy of electron shells, nature of ferromagnetism, ...).

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**Pauli exclusion principle**— n. [after PAULI Wolfgang] the principle that no two electrons, protons, etc. in a given system can have the same set of quantum numbers and, thus, that no two can occupy the same space at the same time: see FERMION … English World dictionary**Pauli exclusion principle**— Physics. See exclusion principle. [1925 30; named after W. PAULI] * * * Assertion proposed by Wolfgang Pauli that no two electrons in an atom can be in the same state or configuration at the same time. It accounts for the observed patterns of… … Universalium**Pauli exclusion principle**— exclusion principle, principle put forward by the Austrian physicist Wolfgang Pauli that no two electrons in an atom can be exactly equivalent … English contemporary dictionary**Pauli exclusion principle**— noun Etymology: Wolfgang Pauli Date: 1926 exclusion principle called also Pauli principle … New Collegiate Dictionary**Pauli exclusion principle**— Pau′li exclu′sion prin ciple n. phs exclusion principle • Etymology: 1925–30; after W. Pauli … From formal English to slang**Pauli exclusion principle**— [ paʊli] noun Physics the assertion that no two fermions can have the same quantum number. Origin 1920s: named after the American physicist Wolfgang Pauli … English new terms dictionary**Pauli exclusion principle**— n. Physics the assertion that no two fermions can have the same quantum number. Etymology: W. Pauli, Austrian physicist d. 1958 … Useful english dictionary**Pauli exclusion principle**— noun A principle in quantum mechanics that states that no two identical fermions may occupy the same quantum state simultaneously … Wiktionary**Exclusion principle**— may refer to: * The Exclusion principle, an epistemological principle * In economics, the exclusion principle states the owner of a private good may exclude others from use unless they pay. * The Pauli exclusion principle, a quantum mechanical… … Wikipedia**exclusion principle**— n. PAULI EXCLUSION PRINCIPLE … English World dictionary