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Spin (physics)
Spin is a conserved quantity carried by elementary particles, and thus by composite particles (hadrons) and atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being ''orbital angular momentum''. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies. For photons, spin is the quantum-mechanical counterpart of the polarization of light; for electrons, the spin has no classical counterpart. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The existence of the electron spin can also be inferred theoretically from the spin–statistics theorem and from the Pauli exclusion principle—and ...
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Conserved Quantity
In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables, the value of which remains constant along each trajectory of the system. Not all systems have conserved quantities, and conserved quantities are not unique, since one can always produce another such quantity by applying a suitable function, such as adding a constant, to a conserved quantity. Since many laws of physics express some kind of conservation, conserved quantities commonly exist in mathematical models of physical systems. For example, any classical mechanics model will have mechanical energy as a conserved quantity as long as the forces involved are conservative. Differential equations For a first order system of differential equations :\frac = \mathbf f(\mathbf r, t) where bold indicates vector quantities, a scalar-valued function ''H''(r) is a conserved quantity of the system if, for all time and initial conditions in some specific domain, :\frac = 0 Note that ...
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Metre
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefixed forms are also used relatively frequently. The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately  km. In 1799, the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the path travelled by light in a vacuum in of a second. After the 2019 redefiniti ...
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Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics. He served as doctoral supervisor for many Nobel Prize winners in physics and chemistry (only J. J. Thomson's record of mentorship is comparable to his). He introduced the second quantum number ( azimuthal quantum number) and the third quantum number ( magnetic quantum number). He also introduced the fine-structure constant and pioneered X-ray wave theory. Early life and education Sommerfeld was born in 1868 to a family with deep ancestral roots in Prussia. His mother Cäcilie Matthias (1839–1902) was the daughter of a Potsdam builder. His father Franz Sommerfeld (1820–1906) was a physician from a leading family in Königsberg, where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Court Pos ...
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Niels Bohr
Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. Bohr was also a philosopher and a promoter of scientific research. Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. Although the Bohr model has been supplanted by other models, its underlying principles remain valid. He conceived the principle of complementarity: that items could be separately analysed in terms of contradictory properties, like behaving as a wave or a stream of particles. The notion of complementarity dominated Bohr's thinking in both science and philosophy. Bohr founded the Institute of Theoretical Physics at the University of ...
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Old Quantum Theory
The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as the semi-classical approximation to modern quantum mechanics. The main and final accomplishments of the old quantum theory were the determination of the modern form of the periodic table by Edmund Stoner and the Pauli Exclusion Principle which were both premised on the Arnold Sommerfeld enhancements to the Bohr model of the atom. The main tool of the old quantum theory was the Bohr–Sommerfeld quantization condition, a procedure for selecting out certain states of a classical system as allowed states: the system can then only exist in one of the allowed states and not in any other state. History The old quantum theory was instigated by the 1900 work of Max Planck on the emission and absorption of light in a ...
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Leiden University
Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Leiden for its defence against Spanish attacks during the Eighty Years' War. As the oldest institution of higher education in the Netherlands, it enjoys a reputation across Europe and the world. Known for its historic foundations and emphasis on the social sciences, the university came into particular prominence during the Dutch Golden Age, when scholars from around Europe were attracted to the Dutch Republic due to its climate of intellectual tolerance and Leiden's international reputation. During this time, Leiden became the home to individuals such as René Descartes, Rembrandt, Christiaan Huygens, Hugo Grotius, Baruch Spinoza and Baron d'Holbach. The university has seven academic faculties and over fifty subject departments wh ...
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Samuel 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 gro ...
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George 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 recei ...
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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 Cathol ...
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Dimensional Analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units. ''Commensurable'' physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and ...
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Reduced Planck Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribu ...
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Dimensionless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field o ...
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