Spin Magnetic Moment
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Spin Magnetic Moment
In physics, mainly quantum mechanics and particle physics, a spin magnetic moment is the magnetic moment caused by the spin of elementary particles. For example, the electron is an elementary spin-1/2 fermion. Quantum electrodynamics gives the most accurate prediction of the anomalous magnetic moment of the electron. In general, a magnetic moment can be defined in terms of an electric current and the area enclosed by the current loop. Since angular momentum corresponds to rotational motion, the magnetic moment can be related to the orbital angular momentum of the charge carriers in the constituting current. However, in magnetic materials, the atomic and molecular dipoles have magnetic moments not just because of their quantized orbital angular momentum, but also due to the spin of elementary particles constituting them. "Spin" is a non-classical property of elementary particles, since classically the "spin angular momentum" of a material object is really just the total ''orb ...
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Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ...
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Neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave similarly within the nucleus, and each has a mass of approximately one atomic mass unit, they are both referred to as nucleons. Their properties and interactions are described by nuclear physics. Protons and neutrons are not elementary particles; each is composed of three quarks. The chemical properties of an atom are mostly determined by the configuration of electrons that orbit the atom's heavy nucleus. The electron configuration is determined by the charge of the nucleus, which is determined by the number of protons, or atomic number. The number of neutrons is the neutron number. Neutrons do not affect the electron configuration, but the sum of atomic and neutron numbers is the mass of the nucleus. Atoms of a chemical element t ...
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Dirac Equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine structure of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, ''antimatter'', previously unsuspected and unobserved and which was experimentally confirmed several years later. It also provided a ''theoretical'' justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theo ...
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Paul Dirac
Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the University of Cambridge, a professor of physics at Florida State University and the University of Miami, and a 1933 Nobel Prize recipient. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics. Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert ...
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Wolfgang Pauli
Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. 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". The discovery involved spin theory, which is the basis of a theory of the structure of matter. Early years Pauli was born in Vienna to a chemist, Wolfgang Joseph Pauli (''né'' Wolf Pascheles, 1869–1955), and his wife, Bertha Camilla Schütz; his sister was Hertha Pauli, a writer and actress. Pauli's middle name was given in honor of his godfather, physicist Ernst Mach. Pauli's paternal grandparents were from prominent families of Prague; his great-grandfather was the publisher Wolf Pascheles. Pauli's mother, Bertha Schütz, was raised in her mother's Roman Catholic religion; Pauli was raised as a Roman Catholic, ...
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Ralph Kronig
Ralph Kronig (10 March 1904 – 16 November 1995) was a German physicist. He is noted for the discovery of particle spin and for his theory of X-ray absorption spectroscopy. His theories include the Kronig–Penney model, the Coster–Kronig transition and the Kramers–Kronig relations. Background Ralph Kronig (later Ralph de Laer Kronig) was born on 10 March 1904 to German parents (Harold Theodor Kronig, Augusta de Laer) in Dresden, Germany. He died in Zeist on 16 November 1995 at the age of 91. Kronig received his primary and high-school education in Dresden and went to New York City to study at Columbia University where he received his PhD in 1925 and subsequently became instructor (1925) and assistant professor (1927). Early in Kronig's career he had encountered Paul Ehrenfest who, while visiting America in 1924, had advised the young physicist Ralph Kronig to revisit Europe. Kronig left for that continent later in 1924 and paid visits to the important centers for theoreti ...
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Hyperfine Splitting
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds. In atoms, hyperfine structure arises from the energy of the nuclear magnetic dipole moment interacting with the magnetic field generated by the electrons and the energy of the nuclear electric quadrupole moment in the electric field gradient due to the distribution of charge within the atom. Molecular hyperfine structure is generally dominated by these two effects, but also includes the energy associated with the interaction between the magnetic moments associated with different magnetic nuclei in a molecule, as well as between the nuclear magnetic moments and the magnetic field generated by the rotation of the molecule. Hyperfine structure contrasts with ''fine structure'', which results from the interaction be ...
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Samuel Abraham Goudsmit
Samuel Abraham Goudsmit (July 11, 1902 – December 4, 1978) was a Dutch-American physicist famous for jointly proposing the concept of electron spin with George Eugene Uhlenbeck in 1925. Life and career Goudsmit was born in The Hague, Netherlands, of Dutch Jewish descent. He was the son of Isaac Goudsmit, a manufacturer of water-closets, and Marianne Goudsmit-Gompers, who ran a millinery shop. In 1943, his parents were deported to a concentration camp by the German occupiers of the Netherlands and were murdered there. Goudsmit studied physics at the University of Leiden under Paul Ehrenfest, where he obtained his PhD in 1927. After receiving his PhD, Goudsmit served as a Professor at the University of Michigan between 1927 and 1946. In 1930 he co-authored a text with Linus Pauling titled ''The Structure of Line Spectra.'' During World War II he worked at the Massachusetts Institute of Technology. As scientific head of the Alsos Mission, he successfully reached a German grou ...
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George Eugene Uhlenbeck
George Eugene Uhlenbeck (December 6, 1900 – October 31, 1988) was a Dutch-American theoretical physicist. Background and education George Uhlenbeck was the son of Eugenius and Anne Beeger Uhlenbeck. He attended the Hogere Burgerschool (High School) in The Hague, from which he graduated in 1918. He subsequently entered Delft University of Technology as a student in chemical engineering. During the next year, he transferred to the Leiden University, to study physics and mathematics, and he earned his bachelor's degree in 1920 (Dutch: ''Kandidaatsexamen''). Uhlenbeck was then admitted by Ehrenfest (a student of Boltzmann's) to the Wednesday evening physics colloquium in Leiden. Ehrenfest became the most important scientific influence in his life. From 1922 to 1925 Uhlenbeck was the tutor of the younger son of the Dutch ambassador in Rome. While there, he attended lectures by Tullio Levi-Civita and Vito Volterra and met his longtime friend, Enrico Fermi. In 1923, Uhlenbeck receive ...
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Wave–particle Duality
Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote: Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger and many others, current scientific theory holds that all particles exhibit a wave nature and vice versa. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected. Although the use of the wave–particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved; see interpretations of quantum mechanics. Bohr regarded the "duality ...
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Elementary Particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, antiquarks, and antileptons, which generally are matter particles and antimatter particles), as well as the fundamental bosons ( gauge bosons and the Higgs boson), which generally are force particles that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle. Ordinary matter is composed of atoms, once presumed to be elementary particles – ''atomos'' meaning "unable to be cut" in Greek – although the atom's existence remained controversial until about 1905, as some leading physicists regarded molecules as mathematical illusions, and matter as ultimately composed of energy. Subatomic constituents of the atom were first identified in the early 1930s; the electron and the proto ...
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Angular Momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, frisbees, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its momentum vector; the latter is in Newtonian mechanics. Unlike linear momentum, angular m ...
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