Quantum physics

Quantum mechanics

Introduction to... Mathematical formulation of... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... Quantum mechanics (QM, or quantum theory) is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ...

Fundamental concepts

Decoherence · Interference Uncertainty · Exclusion Transformation theory Ehrenfest theorem · Measurement Superposition · Entanglement In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... For other uses, see Interference (disambiguation). ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... Quantum superposition is the application of the superposition principle to quantum mechanics. ... It has been suggested that Quantum coherence be merged into this article or section. ...

Experiments

Double-slit experiment Davisson-Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Double-slit diffraction and interference pattern The double-slit experiment consists of letting light diffract through two slits, which produces fringes or wave-like interference patterns on a screen. ... In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. ... In quantum mechanics, the Stern–Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ... In quantum mechanics, Bells Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but can in certain circumstances be violated under quantum mechanics (QM). ... Poppers experiment is an experiment proposed by the 20th century philosopher of science Karl Popper, to test the standard interpretation (the Copenhagen interpretation) of Quantum mechanics. ... Schrödingers Cat: When the nucleus (bottom left) decays, the Geiger counter (bottom centre) may sense it and trigger the release of the gas. ...

Equations

Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... The Pauli equation is a Schrödinger equation which handles spin. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the Schrödinger equation. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...

Advanced theories

Quantum field theory Wightman axioms Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram Quantum field theory (QFT) is the quantum theory of fields. ... In physics the Wightman axioms are an attempt of mathematically stringent, axiomatic formulation of quantum field theory. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ...

Interpretations

Copenhagen · Ensemble Hidden variables · Transactional Many-worlds · Consistent histories Quantum logic Consciousness causes collapse It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ... In physics, a hidden variable theory is urged by a minority of physicists who argue that the statistical nature of quantum mechanics implies that quantum mechanics is incomplete; it is really applicable only to ensembles of particles; new physical phenomena beyond quantum mechanics are needed to explain an individual event. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The many-worlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome to every event to... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ...

Scientists

Planck · Schrödinger Heisenberg · Bohr · Pauli Dirac · Bohm · Born de Broglie · von Neumann Einstein · Feynman Everett · Penrose · Others “Planck” redirects here. ... Schrödinger in 1933, when he was awarded the Nobel Prize in Physics Bust of Schrödinger, in the courtyard arcade of the main building, University of Vienna, Austria. ... Werner Karl Heisenberg (December 5, 1901 – February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... Niels Henrik David Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... This article is about the Austrian-Swiss physicist. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... David Bohm. ... Max Born (December 11, 1882 in Breslau – January 5, 1970 in Göttingen) was a mathematician and physicist. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892–March 19, 1987), was a French physicist and Nobel Prize laureate. ... For other persons named John Neumann, see John Neumann (disambiguation). ... “Einstein” redirects here. ... This article is about the physicist. ... Hugh Everett III (November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation(MWI) of quantum physics, which he called his relative state formulation. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... Below is a list of famous physicists. ...

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The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. This principle is significant, because it explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same time allowing light and radiation to pass. It states that no two identical fermions may occupy the same quantum 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. For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... This article is about the Austrian-Swiss physicist. ... Year 1925 (MCMXXV) was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar. ... Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. ... Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ... Probability densities for the electron at different quantum numbers (l) In quantum mechanics, the quantum state of a system is a set of numbers that fully describe a quantum system. ... In linear algebra, a skew-symmetric (or antisymmetric) matrix is a square matrix A whose transpose is also its negative; that is, it satisfies the equation: AT = −A or in component form, if A = (aij): aij = − aji   for all i and j. ...

The Pauli exclusion principle mathematically follows from applying the rotation operator to two identical particles with half-integer spin. This article concerns the rotation operator, as it appears in quantum mechanics. ... In mathematics, a half-integer is a number of the form , where is an integer. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ...

Overview

The Pauli exclusion principle is one of the most important principles in physics, primarily because the three types of particles from which ordinary matter is made—electrons, protons, and neutrons—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. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... This article is about matter in physics and chemistry. ... For other uses, see Electron (disambiguation). ... For other uses, see Proton (disambiguation). ... This article or section does not adequately cite its references or sources. ... The Periodic Table redirects here. ...

The Pauli exclusion principle follows mathematically from the definition of the angular momentum operator (rotation operator) in quantum mechanics. The exchange of particles in the system of two identical particles (which is mathematically equivalent to the rotation of each particle by 180 degrees) results either in the change of the sign of wave function of the system (when the particles have half-integer spin) or not (when the particles have integer spin). Thus, no two identical particles of half integer spin can be at the same quantum place - because the wave function of such system must be equal to its opposite - and the only wave function which satisfies this condition is the zero wave function. In quantum mechanics, angular momentum is defined like momentum - not as a quantity but as an operator on the wave function: where r and p are the position and momentum operators respectively. ... This article concerns the rotation operator, as it appears in quantum mechanics. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ... In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. ... For other uses, see Boson (disambiguation). ...

Particles with antisymmetric wave functions are called fermions—and obey the Pauli exclusion principle. Apart from the familiar electron, proton and neutron, these include neutrinos and quarks (from which protons and neutrons are made), as well as some atoms like helium-3. All fermions possess "half-integer spin", meaning that they possess an intrinsic angular momentum whose value is (Planck's constant divided by 2π) times a half-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 on identical particles. For the novel, see The Elementary Particles. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... For other uses, see Neutrino (disambiguation). ... For other uses, see Quark (disambiguation). ... Properties For other meanings of Atom, see Atom (disambiguation). ... Helium-3 is a non-radioactive and light isotope of helium. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... This gyroscope remains upright while spinning due to its angular momentum. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... In mathematics, a half-integer is a number of the form , where is an integer. ... Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. ...

Particles with integer spin have a symmetric wave function and are called bosons; in contrast to fermions, they may share the same quantum states. Examples of bosons include the photon and the W and Z bosons. In particle physics, bosons, named after Satyendra Nath Bose, are particles having integer spin. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... In physics, the W and Z bosons are the elementary particles that mediate the weak nuclear force. ...

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 The Atom and the Molecule by Gilbert 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 1922 Niels Bohr showed that the periodic table could be explained by assuming that certain numbers of electrons (for example 2, 8 and 18) corresponded to stable "closed shells". Lewis in the Berkeley Lab Gilbert Newton Lewis (October 23, 1875-March 23, 1946) was a famous American physical chemist. ... The cubical atom was an early atomic model developed by Gilbert N. Lewis in 1916 to account for the phenomenon of valency. ... Niels Henrik David Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... The Periodic Table redirects here. ...

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 in ferromagnetism. He found an essential clue in a 1924 paper by E.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 rare gases 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 by Samuel Goudsmit and George Uhlenbeck as electron spin. In science, an empirical relationship is one based on observation rather than theory: that is, there is no theoretical reason to believe that a relationship should be as claimed; only data that indicates it is. ... The Zeeman effect (IPA ) is the splitting of a spectral line into several components in the presence of a magnetic field. ... Extremely high resolution spectrogram of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter. ... Ferromagnetism is the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field. ... Edmund Clifton Stoner (born October 2, 1899, in Surrey, England; died December 27, 1968 in Leeds, England) was a British theoretical physicist. ... In atomic physics, the principal quantum number symbolized as n is the first quantum number of an atomic orbital. ... The alkali metals are a series of elements comprising Group 1 (IUPAC style) of the periodic table: lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr). ... The energy levels of two or more physical states are said to be degenerate when they have the same value. ... The noble gases are the chemical elements in group 18 (old-style Group 0) of the periodic table. ... Samuel Goudsmit (1902–1978) was a Dutch-American physicist famous for jointly proposing the concept of electron spin with George Eugene Uhlenbeck. ... George Eugene Uhlenbeck (1900 - 1988) was a U.S. (Indonesian-born) physicist. ... In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. ...

Connection to quantum state symmetry

The Pauli exclusion principle can be derived starting from the assumption that a system of particles occupy antisymmetric quantum states. 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. The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ...

As discussed in the article on identical particles, an antisymmetric two-particle state in which one particle exists in state (nota) and the other in state is Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. ... Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ...

However, if and are just the same state, the above formula gives the zero set:

This does not represent a valid quantum state, because the state vectors representing quantum states must be normalizable to 1. In other words, we can never find the particles in this system occupying the same quantum state. In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. ...

Consequences

The Pauli exclusion principle helps explain a wide variety of physical phenomena. One such phenomenon is the "rigidity" or "stiffness" of ordinary matter (fermions): the principle states that identical fermions cannot be squeezed into each other (cf. Young and bulk moduli of solids), hence our everyday observations in the macroscopic world that material objects collide rather than passing straight through each other, and that we are able to stand on the ground without sinking through it. Another consequence of the principle is the elaborate electron shell structure of atoms and of the way atoms share electron(s) - thus variety of chemical elements and of their combinations (chemistry). (An electrically neutral atom contains bound electrons 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). This article does not adequately cite its references or sources. ... The bulk modulus (K) of a substance essentially measures the substances resistance to uniform compression. ... Example of a sodium electron shell model An electron shell, also known as a main energy level, is a group of atomic orbitals with the same value of the principal quantum number n. ... Properties For other meanings of Atom, see Atom (disambiguation). ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... For other uses, see Electron (disambiguation). ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ...

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 (or eigenvalues). In a lithium 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. For other uses, see Helium (disambiguation). ... In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue. ... This article is about the chemical element named Lithium. ... The Periodic Table redirects here. ...

In conductors and semi-conductors free electrons have to share entire bulk space - thus their energy levels are stacking up creating band structure out of each atomic energy level. In strong conductors (metals) electrons are so degenerate that they can not even contribute much into thermal capacity of a metal. Many mechanical, electrical, magnetic, optical and chemical properties of solids are the direct consequence of Pauli repulsion of free and semi-free electrons. In science and engineering, conductors, such as copper or aluminum, are materials with atoms having loosely held valence electrons. ... A semiconductor is a material that is an insulator at very low temperature, but which has a sizable electrical conductivity at room temperature. ... In physics, the free electron model is a possible model for the behaviour of electrons in a crystal structure. ... In solid state physics, the electronic band structure, or simply band structure, refers to the dispersion relation (the relation between energy versus momentum) of electrons in a crystal. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... This article is about metallic materials. ... The energy levels of two or more physical states are said to be degenerate when they have the same value. ... Heat capacity (abbreviated Cth or just C, also called thermal capacity) is the ability of matter to store heat. ...

Astronomy provides another spectacular demonstration of this effect, in the form of white dwarf stars and neutron stars. 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 as degenerate matter. In white dwarfs, the atoms are held apart by the degeneracy pressure of the electrons. In neutron stars, which exhibit even larger gravitational forces, the electrons have merged with the protons to form neutrons, which produce a larger degeneracy pressure. Neutrons are the most "rigid" objects known - their Young modulus (or more accurately, bulk modulus) is 20 orders of magnitude larger than that of diamond. This article or section does not adequately cite its references or sources. ... For the Hugo Award-winning story by Larry Niven, see Neutron Star (story). ... Gravity is a force of attraction that acts between bodies that have mass. ... Degenerate matter is matter which has sufficiently high density that the dominant contribution to its pressure arises from the Pauli exclusion principle. ... For other uses, see Electron (disambiguation). ... For other uses, see Proton (disambiguation). ... This article or section does not adequately cite its references or sources. ... This article does not adequately cite its references or sources. ... The bulk modulus (K) of a substance essentially measures the substances resistance to uniform compression. ...

According to general relativity, in the centers of black holes the gravitational forces would become so intense that everything would break down into fundamental particles, which are supposedly point-like with no internal structure. All of these particles could then pile up at one zero-dimensional point because the gravitational forces would be greater than the degeneracy pressure . This would seem to violate the Pauli exclusion principle, but since the interiors of black holes are beyond the event horizon, and thus inaccessible to experimental verification, this hypothesis remains untested. ^{[citation needed]} For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... This article is about the astronomical body. ... For the science fiction film, see Event Horizon (film). ...

See also

• Exchange force
• Exchange interaction
• Exchange symmetry
• Hund's rule

Exchange interaction is the quantum mechanical effect of increasing or decreasing the energy of two or more fermions when their wave functions overlap. ... In physics, the exchange interaction is a quantum mechanical effect which increases or decreases the energy of two or more electrons when their wave functions overlap. ... Exchange symmetry is derived from a fundamental postulate of quantum statistics, which states that no observable physical quantity should change after exchanging two identical particles. ... Hunds rule is a principle of physical chemistry which states that before any two electrons occupy an orbital in a subshell, other orbitals in the same subshell must first each contain one electron. ...

References

• Dill, Dan (2006). "Chapter 3.5, Many-electron atoms: Fermi holes and Fermi heaps", Notes on General Chemistry (2nd ed.). W. H. Freeman. ISBN 1-4292-0068-5. 
• Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X. 
• Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 0-8053-8714-5. 
• Massimi, Michela (2005). Pauli's Exclusion Principle. Cambridge University Press. ISBN 0-521-83911-4. 
• Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman. ISBN 0-7167-4345-0. 

Richard L. Liboff is a U.S. physicist who has authored five books and nearly 150 other publications in variety of fields, including plasma physics, planetary physics, cosmology, quantum chaos, and quantum billiards. ...

External links

• Nobel Lecture: Exclusion Principle and Quantum Mechanics Pauli's own account of the development of the Exclusion Principle.
• The Exclusion Principle (1997), Pauli's exclusion rules vs. the Aspden exclusion rules, radiation factor, Larmor radiation formula, elliptical motion, quantum states, electron shells, nature of ferromagnetism, etc.