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Encyclopedia > Spin (physics)

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. In classical mechanics, the spin angular momentum of a body is associated with the rotation of the body around its own center of mass. For example, the spin of the Earth is associated with its daily rotation about the polar axis. On the other hand, the orbital angular momentum of the Earth is associated with its annual motion around the Sun. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Gyroscope. ... The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum. ... In physics, the center of mass (or centre of mass) of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... A sphere rotating around its axis. ... Earth (IPA: , often referred to as the Earth, Terra, or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... For other uses of the word pole, see Pole (disambiguation). ... A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... The Sun is the star of our solar system. ...

In quantum mechanics, spin is particularly important for systems at atomic length scales, such as individual atoms, protons, or electrons. Such particles and the spin of quantum mechanical systems ("particle spin") possesses several unusual or non-classical features, and for such systems, spin angular momentum cannot be associated with rotation but instead refers only to the presence of angular momentum. Fig. ... Properties For other articles with similar names, see Atom (disambiguation). ... Properties For other articles with similar names, see Atom (disambiguation). ... Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... The electron is a fundamental subatomic particle that carries an electric charge. ...

(Note: This article uses the term "particle" to refer to quantum mechanical systems, with the understanding that such actually exhibit wave-particle duality, and thus display both particle-like and wave-like behaviors.)

In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ... A wave is a disturbance that propagates through space or spacetime, often transferring energy. ...

## Spin of elementary and composite particles GA_googleFillSlot("encyclopedia_square");

One of the most remarkable discoveries associated with quantum physics is the fact that elementary particles can possess non-zero spin. Elementary particles are particles that cannot be divided into any smaller units, such as the photon, the electron, and the various quarks. Theoretical and experimental studies have shown that the spin possessed by these particles cannot be explained by postulating that they are made up of even smaller particles rotating about a common center of mass (see classical electron radius); as far as we can tell, these elementary particles are true point particles. The spin that they carry is a truly intrinsic physical property, akin to a particle's electric charge and mass. In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, microwaves, radio waves, and visible light are all forms of light. ... The electron is a fundamental subatomic particle that carries an electric charge. ... These are the 6 quarks and their most likely decay modes. ... The classical electron radius, also known as the Compton radius or the Thomson scattering length is based on a classical (i. ... A point particle is an idealized particle heavily used in physics. ...

The concept of elementary particle spin was first proposed in 1925 by Ralph Kronig, George Uhlenbeck, and Samuel Goudsmit. A later section covers the history of this hypothesis and its subsequent developments. 1925 (MCMXXV) was a common year starting on Thursday (link will take you to calendar). ... Ralph Kronig Ralph Kronig was a German-American physicist (1904-1995). ... George Eugene Uhlenbeck (1900 - 1988) was a U.S. (Indonesian-born) physicist. ... Samuel Goudsmit (1902&#8211;1978) was a Dutch-American physicist famous for jointly proposing the concept of electron spin with George Eugene Uhlenbeck. ...

According to quantum mechanics, the angular momentum of any system is quantized. The magnitude of angular momentum can only take on the values according to this relation: Fig. ... Gyroscope. ... In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ... // Real numbers The magnitude of a real number is usually called the absolute value or modulus. ...

$L = hbar , sqrt{s (s+1)},$

where $hbar$ is the reduced Planck's constant, and s is a non-negative integer or half-integer (0, 1/2, 1, 3/2, 2, etc.). For instance, electrons (which are elementary particles) are called "spin-1/2" particles because their intrinsic spin angular momentum has s = 1/2. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... The integers consist of the positive natural numbers (1, 2, 3, â€¦), their negatives (âˆ’1, âˆ’2, âˆ’3, ...) and the number zero. ... In mathematics, a half-integer is a number of the form , where is an integer. ...

The spin carried by each elementary particle has a fixed s value that depends only on the type of particle, and cannot be altered in any known way (although, as we will see, it is possible to change the direction in which the spin "points".) Every electron in existence possesses s = 1/2. Other elementary spin-1/2 particles include neutrinos and quarks. On the other hand, photons are spin-1 particles, whereas the hypothetical graviton is a spin-2 particle. The neutrino is an elementary particle. ... These are the 6 quarks and their most likely decay modes. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, microwaves, radio waves, and visible light are all forms of light. ... This article or section is in need of attention from an expert on the subject. ...

The spin of composite particles, such as protons, neutrons, atomic nuclei, and atoms, is made up of the spins of the constituent particles, and their total angular momentum is the sum of their spin and the orbital angular momentum of their motions around one another. The angular momentum quantization condition applies to both elementary and composite particles. Composite particles are often referred to as having a definite spin, just like elementary particles; for example, the proton is a spin-1/2 particle. This is understood to refer to the spin of the lowest-energy internal state of the composite particle (i.e., a given spin and orbital configuration of the constituents). It is not always easy to deduce the spin of a composite particle from first principles; for example, even though we know that the proton is a spin-1/2 particle, the question of how this spin is distributed among the three internal quarks and the surrounding gluons is an active area of research. Elementary particles An elementary particle is a particle with no measurable internal structure, that is, it is not a composite of other particles. ... Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... This article or section does not cite its references or sources. ... A semi-accurate depiction of the helium atom. ... Properties For other articles with similar names, see Atom (disambiguation). ... Nucleons (protons and neutrons) are spin=1/2 subatomic particles, composed of quarks. ... These are the 6 quarks and their most likely decay modes. ... In particle physics, gluons are vector gauge bosons that mediate strong color charge interactions of quarks in quantum chromodynamics (QCD). ...

## Spin direction

In classical mechanics, the angular momentum of a particle possesses not only a magnitude (how fast the body is rotating), but also a direction (the axis of rotation of the particle). Quantum mechanical spin also contains information about direction, but in a more subtle form. Quantum mechanics states that the component of angular momentum measured along any direction (say along the z-axis) can only take on the values The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ... In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ...

$hbar s_z, qquad s_z = - s, - s + 1, cdots, s$

where s is the principal spin quantum number discussed in the previous section. One can see that there are 2s+1 possible values of sz. For example, there are only two possible values for a spin-1/2 particle: sz = +1/2 and sz = -1/2. These correspond to quantum states in which the spin is pointing in the +z or -z directions respectively, and are often referred to as "spin up" and "spin down". See spin-1/2. A quantum state is any possible state in which a quantum mechanical system can be. ... In quantum mechanics, spin is an intrinsic property of all elementary particles. ...

For a given quantum state , it is possible to describe a spin vector $lang S rang$ whose components are the expectation values of the spin components along each axis, i.e., $lang S rang = [lang s_x rang, lang s_y rang, lang s_z rang]$. This vector describes the "direction" in which the spin is pointing, corresponding to the classical concept of the axis of rotation. It turns out that the spin vector is not very useful in actual quantum mechanical calculations, because it cannot be measured directly — sx, sy and sz cannot possess simultaneous definite values, because of a quantum uncertainty relation between them. As a qualitative concept, however, the spin vector is often handy because it is easy to picture classically. In probability (and especially gambling), the expected value (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical odds are... The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ... In quantum physics, the Heisenberg uncertainty principle or the Heisenberg indeterminacy principle â€” the latter name given to it by Niels Bohr â€” states that when measuring conjugate quantities, which are pairs of observables of a single elementary particle, increasing the accuracy of the measurement of one quantity increases the uncertainty of...

For instance, quantum mechanical spin can exhibit phenomena analogous to classical gyroscopic effects. For example, one can exert a kind of "torque" on an electron by putting it in a magnetic field (the field acts upon the electron's intrinsic magnetic dipole moment — see the following section). The result is that the spin vector undergoes precession, just like a classical gyroscope. A gyroscope is a device for measuring or maintaining orientation, based on the principle of conservation of angular momentum. ... In physics, torque can be thought of informally as rotational force. The SI units for Torque are newton meters although centinewton meters (cNÂ·m), foot-pounds force (ftÂ·lbf), inch pounds (lbfÂ·in) and inch ounces (ozfÂ·in) are also frequently used expressions of torque. ... To meet Wikipedias quality standards, this article may require cleanup. ... In physics, the magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. ... Precession refers to a change in the direction of the axis of a rotating object. ...

Mathematically, quantum mechanical spin is not described by a vector as in classical angular momentum. It is described using a family of objects known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-1/2 particle by 360 degrees does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720 degree rotation! In physics and in vector calculus, a spatial vector is a concept characterized by a magnitude, which is a scalar, and a direction (which can be defined in a 3-dimensional space by the Euler angles). ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In linear algebra and geometry, a coordinate rotation is a type of transformation from one system of coordinates to another system of coordinates such that distance between any two points remains invariant under the transformation. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

## Spin and magnetic moment

Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern-Gerlach experiment, or by measuring the magnetic fields generated by the particles themselves. In physics, the magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Classical electromagnetism is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. ... To meet Wikipedias quality standards, this article may require cleanup. ... In quantum mechanics, the Sternâ€“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. ...

The intrinsic magnetic moment μ of a particle with charge q, mass m, and spin S, is

$mu = g , frac{q}{2m}, S$

where the dimensionless quantity g is called the gyromagnetic ratio or g-factor. In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... In physics, the gyromagnetic ratio or LandÃ© g-factor is a dimensionless unit which expresses the ratio of the magnetic dipole moment to the angular momentum of an elementary particle or atomic nucleus. ...

The electron, despite being an elementary particle, possesses a nonzero magnetic moment. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron g-factor, which has been experimentally determined to have the value 2.0023193043768(86), with the first 12 figures certain. The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.00231930437... arises from the electron's interaction with the surrounding electromagnetic field, including its own field. In atomic physics, the magnetic dipole moment of an electron is involved in a variety of important atomic processes and effects. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... In physics, the LandÃ© g-factor, , relates the magnetic dipole moment to the angular momentum of a quantum state. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... This article or section may be confusing or unclear for some readers, and should be edited to rectify this. ...

Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle. In fact, it is made up of quarks, which are charged particles. The magnetic moment of the neutron comes from the moments of the individual quarks and their orbital motions. For other uses of this term, see: Quark (disambiguation) 1974 discovery photograph of a possible charmed baryon, now identified as the &#931;c++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ...

The neutrinos are both elementary and electrically neutral, and theory indicates that they have zero magnetic moment. The measurement of neutrino magnetic moments is an active area of research. As of 2003, the latest experimental results have put the neutrino magnetic moment at less than 1.3 × 10-10 times the electron's magnetic moment. The neutrino is an elementary particle. ... 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January events January 1 Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ...

In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction. In ferromagnetic materials, however, the dipole moments are all lined up with one another, producing a macroscopic, non-zero magnetic field. These are the ordinary "magnets" with which we are all familiar. Materials are inputs to production or manufacturing. ... A ferromagnet is a piece of ferromagnetic material, in which the microscopic magnetized regions, called domains, have been aligned by an external magnetic field (e. ...

The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions. [1] [2] Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. ... The Ising model, named after the physicist Ernst Ising, is a mathematical model in statistical mechanics. ... The Heisenberg model is the case of the n-vector model, one of the models used in Statistical Physics in order to model ferromagnetism and other phenomena. ... In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ...

## The spin-statistics connection

It turns out that the spin of a particle is closely related to its properties in statistical mechanics. Particles with half-integer spin obey Fermi-Dirac statistics, and are known as fermions. They are subject to the Pauli exclusion principle, which forbids them from sharing quantum states, and are described in quantum theory by "antisymmetric states" (see the article on identical particles.) Particles with integer spin, on the other hand, obey Bose-Einstein statistics, and are known as bosons. These particles can share quantum states, and are described using "symmetric states". The proof of this is known as the spin-statistics theorem, which relies on both quantum mechanics and the theory of special relativity. In fact, the connection between spin and statistics is one of the most important and remarkable consequences of special relativity. Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Fermi-Dirac distribution as a function of Îµ/Î¼ plotted for 4 different temperatures. ... In particle physics, fermions are particles with half-integer spin. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. ... A quantum state is any possible state in which a quantum mechanical system can be. ... Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. ... In statistical mechanics, Bose-Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium. ... In particle physics, bosons, named after Satyendra Nath Bose, are particles having integer spin. ... The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

## Applications

Well established applications of spin are nuclear magnetic resonance spectroscopy in chemistry, electron spin resonance spectroscopy in chemistry and physics, magnetic resonance imaging or MRI in medicine, and GMR drive head technology in modern hard disks. Pacific Northwest National Laboratorys high magnetic field (800 MHz, 18. ... Electron Paramagnetic Resonance (EPR) or Electron Spin Resonance (ESR) is a spectroscopic technique which detects species that have unpaired electrons, generally meaning that it must be a free radical, if it is an organic molecule, or that it has transition metal ions if it is an inorganic complex. ... The mri are a fictional alien species in the Faded Sun Trilogy of C.J. Cherryh. ... Founding results of Fert The Giant Magnetoresistance Effect (GMR) is a quantum mechanical effect observed in thin film structures composed of alternating ferromagnetic and nonmagnetic metal layers. ... Typical hard drives of the mid-1990s. ...

A possible application of spin is as a binary information carrier in spin transistors. Electronics based on spin transistors is called spintronics. The magnetically-sensitive transistor (also known as the spin transistor or spintronic transistor--named for spintronics, the technology which this development spawned), originally developed in the 1990s and currently still being developed, is an improved design on the common transistor invented in the 1940s. ... Unsolved problems in physics: Is it possible to construct a practical electronic device that operates on the spin of the electron, rather than its charge? Spintronics (a neologism for spin-based electronics), also known as magnetoelectronics, is an emergent technology which exploits a quantum property of electrons known as spin...

## History

Wolfgang Pauli was possibly the most influential physicist in the theory of spin. Spin was first discovered in the context of the emission spectrum of alkali metals. In 1924 Pauli introduced what he called a "two-valued quantum degree of freedom" associated with the electron in the outermost shell. This allowed him to formulate the Pauli exclusion principle, stating that no two electrons can share the same quantum numbers. This article is about Austrian-Swiss physicist Wolfgang Pauli. ... A materials emission spectrum is the amount of electromagnetic radiation of each frequency it emits when it is heated (or more generally when it is excited). ... The alkali metals are the series of elements in Group 1 (IUPAC style) of the periodic table (excluding hydrogen in all but one rare circumstance): lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr). ... 1924 (MCMXXIV) was a leap year starting on Tuesday (link will take you to calendar). ... 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. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. ...

The physical interpretation of Pauli's "degree of freedom" was initially unknown. Ralph Kronig, one of Landé's assistants, suggested in early 1925 that it was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. This would violate the theory of relativity. Largely due to Pauli's criticism, Kronig decided not to publish his idea. Ralph Kronig Ralph Kronig was a German-American physicist (1904-1995). ... Alfred LandÃ© was a German physicist (1888-1976) known for his contributions to Quantum Theory. ... 1925 (MCMXXV) was a common year starting on Thursday (link will take you to calendar). ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. In metric units, c is exactly 299,792,458 metres per second (1,079,252,848. ... Two-dimensional analogy of space-time distortion described in General Relativity. ...

In the fall of that year, the same thought came to two young Dutch physicists, George Uhlenbeck and Samuel Goudsmit. Under the advice of Paul Ehrenfest, they published their results in a small paper. It met a favorable response, especially after Llewellyn Thomas managed to resolve a factor of two discrepancy between experimental results and Uhlenbeck and Goudsmit's calculations (and Kronig's unpublished ones). This discrepancy was due to the necessity to take into account the orientation of the electron's tangent frame, in addition to its position; mathematically speaking, a fiber bundle description is needed. The tangent bundle effect is additive and relativistic (i.e. it vanishes if c goes to infinity); it is one half of the value obtained without regard for the tangent space orientation, but with opposite sign. Thus the combined effect differs from the latter by a factor two (Thomas precession). George Eugene Uhlenbeck (1900 - 1988) was a U.S. (Indonesian-born) physicist. ... Samuel Goudsmit (1902&#8211;1978) was a Dutch-American physicist famous for jointly proposing the concept of electron spin with George Eugene Uhlenbeck. ... Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 â€“ Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ... Llewellyn Hilleth Thomas born in 1903 died in 1992. ... In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which locally looks like a product of two spaces but may possess a different global structure. ... In mathematics, the tangent bundle of a differentiable manifold M, denoted by T(M) or just TM, is the disjoint union of the tangent spaces to each point of M An element of T(M) is a pair (x,v) where x âˆˆ M and v âˆˆ Tx(M), the tangent space... Thomas precession, named after L.H. Thomas, is a correction to the spin-orbit interaction in Quantum Mechanics, which takes into account the relativistic time dilation between the electron and the nucleus in hydrogenic atoms. ...

Despite his initial objections to the idea, Pauli formalized the theory of spin in 1927, using the modern theory of quantum mechanics discovered by Schrödinger and Heisenberg. He pioneered the use of Pauli matrices as a representation of the spin operators, and introduced a two-component spinor wave-function. 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... Fig. ... Erwin Rudolf Josef Alexander SchrÃ¶dinger (August 12, 1887 â€“ January 4, 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the SchrÃ¶dinger equation, for which he received the Nobel Prize in 1933. ... Werner Heisenberg Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics. ... The Pauli matrices are a set of 2 Ã— 2 complex Hermitian and unitary matrices. ... Group representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

Pauli's theory of spin was non-relativistic. However, in 1928, Paul Dirac published the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a "Dirac spinor") was used for the electron wave-function. 1928 (MCMXXVIII) was a leap year starting on Sunday (link will take you to calendar). ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... The electron is a fundamental subatomic particle that carries an electric charge. ...

In 1940, Pauli proved the spin-statistics theorem, which states that fermions have half-integer spin and bosons integer spin. 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ... The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ...

Gyroscope. ... In particle physics, helicity is the projection of the angular momentum to the direction of motion: Because the angular momentum with respect to an axis has discrete values, helicity is discrete, too. ... The Pauli matrices are a set of 2 Ã— 2 complex Hermitian and unitary matrices. ... In theoretical physics, the Rarita-Schwinger equation is the field equation of spin-3/2 fermions. ... In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple Lie groups. ... 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. ... In quantum mechanics, spin is an intrinsic property of all elementary particles. ... The Euclidean group SE(d) is generated by translations and rotations. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Yrast is a technical term in nuclear physics that refers to a state of a nucleus with more angular momentum than all the states of lower energy. ... Stephen William Hawking, CH, CBE, FRS (born 8 January 1942) is a theoretical physicist. ...

## References

• Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-111892-7.
• Shankar, R. (1994). “chapter 14-Spin”, Principles of Quantum Mechanics (2nd ed.). Springer. ISBN 0-306-44790-8.
• "Spintronics. Feature Article" in Scientific American, June 2002

Scientific American is a popular-science magazine, published monthly since August 28, 1845, making it the oldest continuously published magazine in the United States. ...

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