Meta tags:
Headings (most frequently used words):
spin, of, quantum, pauli, angular, momentum, number, relativistic, and, measurement, along, physics, contents, models, relation, to, orbital, magnetic, moments, direction, mathematical, formulation, parity, measuring, applications, history, see, also, references, further, reading, external, links, rotating, charged, mass, classically, non, describable, two, valuedness, circulation, classical, fields, in, bohmian, mechanics, dirac, electron, fermions, bosons, statistics, theorem, projection, multiplicity, vector, definitions, operator, matrices, exclusion, principle, rotations, lorentz, transformations, the, or, axes, an, arbitrary, axis, compatibility, measurements, higher, spins, intrinsic, theory,
Text of the page (most frequently used words):
the (509), spin (249), and (171), quantum (150), for (87), frac (85), pmatrix (82), displaystyle (69), sqrt (67), that (65), this (57), with (57), #angular (54), are (54), momentum (53), begin (49), end (49), rangle (49), left (47), right (47), particle (46), pauli (44), particles (41), electron (41), physics (39), edit (39), magnetic (39), mechanics (37), can (34), hbar (32), axis (31), isbn (30), have (30), psi (30), from (29), two (29), not (28), which (28), theory (27), 978 (27), state (26), doi (25), integer (24), was (22), rotation (22), number (22), where (22), along (22), same (22), direction (22), bibcode (21), values (21), theta (21), classical (20), sigma (20), fermions (20), hat (20), may (18), has (18), one (18), states (18), known (18), any (18), all (17), field (17), orbital (17), operator (17), representation (17), matrices (17), such (17), vector (17), statistics (16), bosons (16), moment (15), atoms (15), exclusion (15), principle (15), nuclear (15), mathbf (15), history (14), dirac (14), neutrino (14), also (14), only (14), elementary (14), non (13), physical (13), relativistic (13), measurement (13), wave (13), theorem (13), but (13), like (13), half (13), they (13), would (13), about (12), operators (12), group (12), electrons (12), its (12), aligned (12), matrix (11), intrinsic (11), each (11), see (11), rotating (11), gamma (11), boldsymbol (11), langle (11), mechanical (11), energy (10), since (10), atomic (10), section (10), moments (10), model (10), even (10), there (10), example (10), spins (10), dots (10), mass (10), symmetry (9), other (9), parity (9), between (9), however (9), given (9), interpretation (9), component (9), spinor (9), these (9), delta (9), dimensional (9), different (8), stern (8), gerlach (8), function (8), zero (8), john (8), press (8), modern (8), rotations (8), fields (8), their (8), while (8), constant (8), original (8), does (8), equation (8), possible (8), when (8), numbers (8), charged (8), will (8), into (8), article (8), corresponding (8), angle (8), obey (8), wikipedia (7), using (7), sources (7), related (7), information (7), phase (7), hamiltonian (7), time (7), cite (7), university (7), resonance (7), 1103 (7), nuclei (7), mathematical (7), how (7), theories (7), arxiv (7), applied (7), representations (7), value (7), factor (7), classically (7), experiment (7), observed (7), were (7), properties (7), measurements (7), concept (7), associated (7), applications (7), main (7), higher (7), quad (7), irreducible (7), being (7), measured (7), beta (7), sum (7), projection (7), neutron (7), models (7), toggle (6), under (6), terms (6), 2024 (6), many (6), space (6), archived (6), wiley (6), 471 (6), help (6), cambridge (6), further (6), hydrogen (6), wolfgang (6), pdf (6), vol (6), special (6), first (6), photon (6), what (6), odd (6), his (6), degree (6), freedom (6), charge (6), allowed (6), system (6), lorentz (6), important (6), arbitrary (6), product (6), change (6), having (6), big (6), therefore (6), proof (6), textstyle (6), must (6), take (6), possess (6), cannot (6), exist (6), additional (5), use (5), page (5), links (5), articles (5), unsourced (5), retrieved (5), effect (5), machine (5), science (5), interaction (5), point (5), introduction (5), dipole (5), total (5), fundamental (5), 2023 (5), electrodynamics (5), book (5), thomas (5), review (5), 2nd (5), 1927 (5), 2014 (5), after (5), some (5), due (5), then (5), light (5), matter (5), boson (5), studies (5), philosophy (5), describable (5), valuedness (5), transformation (5), experimental (5), been (5), observations (5), result (5), both (5), rules (5), used (5), large (5), called (5), well (5), neutral (5), thus (5), just (5), because (5), transformations (5), unitary (5), alpha (5), equal (5), described (5), discrete (5), planck (5), either (5), table (4), contents (4), search (4), text (4), commons (4), wayback (4), cs1 (4), references (4), 2021 (4), wigner (4), schrödinger (4), imaging (4), chemistry (4), experiments (4), formulation (4), uncertainty (4), out (4), position (4), general (4), goudsmit (4), waves (4), sons (4), december (4), atom (4), 1063 (4), uhlenbeck (4), 1007 (4), new (4), theoretical (4), letters (4), functions (4), 1016 (4), more (4), way (4), fine (4), units (4), bohmian (4), quantized (4), could (4), unlike (4), single (4), results (4), based (4), produced (4), idea (4), than (4), around (4), collection (4), spectroscopy (4), type (4), include (4), those (4), approach (4), photons (4), through (4), often (4), cos (4), sin (4), defined (4), leq (4), array (4), following (4), eigenvalues (4), three (4), axes (4), learn (4), finding (4), probability (4), eigenvalue (4), etc (4), make (4), eigenvectors (4), spinors (4), definite (4), hence (4), rotated (4), though (4), most (4), components (4), electrically (4), composite (4), quarks (4), dependence (4), property (4), hide (4), move (4), sidebar (4), subsection (4), view (3), wikimedia (3), september (3), link (3), wikidata (3), date (3), names (3), list (3), description (3), gravity (3), logic (3), electronics (3), finite (3), choice (3), collapse (3), schwinger (3), heisenberg (3), levels (3), ground (3), lecture (3), datta (3), paul (3), systems (3), princeton (3), physrev (3), 521 (3), spectra (3), set (3), 1985 (3), molecules (3), london (3), series (3), oriented (3), today (3), 1989 (3), 1925 (3), behavior (3), bohr (3), times (3), dover (3), 2013 (3), journal (3), electronic (3), 2008 (3), molecular (3), 582 (3), beams (3), formula (3), 2005 (3), world (3), robert (3), own (3), structure (3), 1940 (3), higgs (3), 184 (3), water (3), polarization (3), correct (3), showed (3), became (3), established (3), clear (3), giving (3), four (3), calculations (3), kronig (3), rest (3), frame (3), order (3), relativity (3), speed (3), starting (3), changes (3), proposed (3), instance (3), nmr (3), determined (3), protons (3), pions (3), case (3), rightarrow (3), inhomogeneous (3), measuring (3), spatial (3), less (3), cdot (3), resulting (3), yield (3), note (3), measure (3), remove (3), message (3), please (3), material (3), challenged (3), removed (3), adding (3), citations (3), reliable (3), improve (3), above (3), vectors (3), normalized (3), down (3), give (3), takes (3), sign (3), negative (3), real (3), scalar (3), phi (3), dagger (3), generic (3), upon (3), fact (3), commutation (3), relations (3), dimension (3), cdots (3), mathematically (3), need (3), identical (3), reduced (3), analogous (3), bring (3), back (3), 180 (3), kind (3), actual (3), them (3), relation (3), multiplicity (3), discussed (3), possesses (3), magnitude (3), masses (3), account (3), standard (3), electromagnetic (3), including (3), occupy (3), generated (3), helium (3), force (3), velocity (3), contrast (3), imply (3), quantization (3), whether (3), circulation (3), tools (3), languages (2), contact (2), privacy (2), policy (2), last (2), hidden (2), categories (2), category (2), german (2), statements (2), february (2), needing (2), maint (2), multiple (2), authors (2), short (2), rotational (2), epr (2), casimir (2), optics (2), network (2), key (2), distribution (2), correction (2), timeline (2), complexity (2), automata (2), technology (2), calculus (2), geometry (2), delayed (2), eraser (2), franck (2), bell (2), broglie (2), bohm (2), consistent (2), interpretations (2), rarita (2), formulations (2), superposition (2), jump (2), interference (2), density (2), invariant (2), ladder (2), nature (2), discovery (2), wikiquote (2), external (2), 2004 (2), scientists (2), engineers (2), leader (2), elliot (2), david (2), 1998 (2), 3rd (2), incompatibility (2), 691 (2), precise (2), method (2), 1877 (2), especially (2), cohen (2), reading (2), resnick (2), eisberg (2), 87373 (2), solids (2), fraser (2), ronald (2), 114 (2), character (2), cross (2), pais (2), abraham (2), george (2), november (2), requirement (2), internal (2), individual (2), oxford (2), 1946 (2), nobel (2), whittaker (2), edmund (2), 486 (2), 26126 (2), aether (2), electricity (2), 1926 (2), magnetism (2), tio (2), 233913 (2), das (2), 1990 (2), analog (2), donald (2), print (2), beam (2), technique (2), 300 (2), sodium (2), 1119 (2), 319 (2), american (2), compact (2), 084 (2), sakurai (2), 4614 (2), publications (2), tung (2), 2020 (2), england (2), scientific (2), 00098975 (2), principles (2), 151802 (2), pmid (2), physrevlett (2), shrock (2), massive (2), 963 (2), 1977 (2), gauge (2), muon (2), 1444 (2), leptons (2), discovered (2), place (2), directly (2), nist (2), 2022 (2), 716 (2), connection (2), 131 (2), ohanian (2), hans (2), 541 (2), actually (2), basel (2), 7643 (2), shpsb (2), part (2), 2019 (2), griffiths (2), spintronics (2), tensor (2), orbit (2), retrospect (2), direct (2), explanation (2), spots (2), suggested (2), erwin (2), always (2), silver (2), contribute (2), published (2), introduced (2), werner (2), discrepancy (2), spectrum (2), now (2), valued (2), continued (2), precession (2), thought (2), physicists (2), immediately (2), ehrenfest (2), initially (2), early (2), self (2), produce (2), necessary (2), context (2), strong (2), periodic (2), transistors (2), referred (2), manipulation (2), leads (2), definition (2), role (2), frequency (2), chemical (2), relies (2), esr (2), deuterium (2), allows (2), analysis (2), show (2), needed (2), representing (2), inversion (2), isotopes (2), includes (2), means (2), simple (2), euler (2), useful (2), products (2), lclc (2), basis (2), taking (2), itself (2), kronecker (2), subsequent (2), our (2), become (2), compatibility (2), obtained (2), usual (2), eigenstates (2), multiplied (2), directions (2), simply (2), respect (2), made (2), eigenvector (2), ambiguity (2), convention (2), chosen (2), element (2), positive (2), preserved (2), transform (2), law (2), shown (2), exp (2), integers (2), corresponds (2), elements (2), small (2), mathcal (2), holds (2), principal (2), coordinate (2), complex (2), projective (2), should (2), amplitudes (2), consequences (2), acting (2), 166 (2), obeys (2), jkl (2), definitions (2), subtle (2), 360 (2), opposite (2), torque (2), looks (2), imagined (2), qualitative (2), picture (2), acts (2), equivalent (2), effects (2), pointing (2), meaning (2), ordinary (2), detector (2), detecting (2), expectation (2), body (2), form (2), lead (2), radiative (2), contributions (2), prevent (2), electroweak (2), neutrinos (2), particular (2), despite (2), comes (2), accurate (2), experimentally (2), digits (2), arises (2), deviation (2), radius (2), dimensionless (2), quantity (2), diagram (2), lines (2), requires (2), derived (2), fermi (2), bose (2), einstein (2), historically (2), although (2), considered (2), require (2), pressure (2), families (2), depends (2), below (2), changed (2), momenta (2), consequently (2), existence (2), free (2), motion (2), pilot (2), wavefields (2), steps (2), abstract (2), required (2), 183 (2), appearance (2), upload (2), file (2), read (2), english (2), norsk (2), bahasa (2), log (2), create (2), donate (2), menu (2), add, topic, mobile, cookie, statement, developers, code, conduct, legal, safety, contacts, disclaimers, available, apply, site, you, agree, registered, trademark, profit, organization, foundation, inc, creative, attribution, sharealike, license, rendered, parsoid, edited, 2026, utc, webarchive, template, errors, language, quantities, https, org, index, php, title, spin_, oldid, 1372723320, yale, lux, israel, czech, republic, japan, bnf, data, france, national, gnd, international, authority, control, databases, mysticism, paradox, friend, popular, culture, cat, statistical, fluctuation, extensions, teleportation, simulator, sensing, programming, neural, metrology, metamaterial, learning, gates, image, processing, error, cryptography, computing, circuit, channel, cellular, bus, amplifier, algorithms, spacetime, stochastic, mind, problem, dynamics, differential, cosmology, chaos, biology, wheeler, popper, elitzur, vaidman, mach, zehnder, interferometer, hertz, double, slit, davisson, germer, test, transactional, relational, objective, worlds, superdeterminism, local, variable, ensemble, copenhagen, histories, consciousness, causes, bayesian, rydberg, majorana, weyl, klein, gordon, equations, path, integral, universal, duality, scattering, tunnelling, nonlocality, decoherence, entanglement, degenerate, excited, level, complementarity, bra, ket, notation, born, rule, fundamentals, glossary, old, background, creation, annihilation, squeeze, ordered, correlator, hanbury, brown, twiss, displacement, transition, electromagnetism, kinetic, anti, symmetric, alembertian, online, 2016, ece, 495n, milestones, 1896, 2025, quotations, media, tipler, 5th, freeman, 7167, 0809, oscillations, thermodynamics, thompson, william, 1994, 55264, illustrated, guide, symmetries, serway, raymond, jewett, 6th, brooks, cole, 534, 40842, 009, 40204, 1017, 9781009402040, jackson, 30932, edmonds, 1957, 07912, hipple, sommer, 1949, determining, faraday, 1878, 1949phrv, 1877h, condon, shortley, 1935, chapter, 09209, tannoudji, claude, diu, bernard, laloë, 2006, volume, 56952, 274, march, 767, 221, 1098, rspa, 0036, 1927rspsa, 212f, 212, proceedings, royal, society, containing, papers, effective, friedrich, herschbach, 2003, 1650229, 2003pht, 56l, 53f, bad, cigar, helped, reorient, 00000199d450d7e8a5bddcd144150000, 881186, 1989pht, 42l, 34p, ersetzung, der, hypothese, vom, unmechanischen, zwang, durch, eine, forderung, bezüglich, des, inneren, verhaltens, jedes, einzelnen, elektrons, replacement, hypothesis, unmechanical, constraint, regarding, 954, bf01558878, 953, die, naturwissenschaften, 1991, clarendon, 852049, 244, niels, prize, repr, york, publ, 1900, assadi, hanaor, study, copper, energetics, polymorphs, 4811539, 2013jap, 113w3913a, 1304, 1854, 113, electrooptic, modulator, 667, 102730, 1990apphl, 665d, 665, perkins, aufl, univ, 62196, high, estermann, july, 323, revmodphys, 1946rvmp, 300e, reviews, rabi, april, 1933, 583, 1933phrv, 582r, hamilton, 1941, 337, 1991712, 1941amjph, 319h, polynomials, 3842, 2014sigma, 084c, 1402, 3541, zachos, fairlie, curtright, jun, napolitano, jim, 2017, 108, 42241, hall, brian, graduate, texts, mathematics, 267, 358, 7115, 7116, 2013qtm, 354, mathematicians, mineola, 540, 874097814, oclc, 306, 51279, messiah, albert, 67053, weinberg, steven, berestetskii, vladimir, 1982, course, butterworth, heinemann, 7506, 3371, pitaevskii, lev, lifshitz, evgeny, quanta, handbook, concepts, atkins, 1974, 855493, nicole, cirigliano, ramsey, musolf, vogel, wise, mark, october, 16241715, 2005phrvl, 95o1802b, hep, 0504134, fujikawa, 1980, 966, 1980phrvl, 963f, lee, benjamin, natural, suppression, violation, lepton, nonconservation, 1473, physrevd, 1977phrvd, 1444l, exotic, decays, heavy, 305, 0370, 2693, 90377, 1977phlb, 303m, 303, b67, sanda, marciano, interactions, 115, years, exactly, slightly, something, 00116, worked, 1948, divided, square, root, alternative, instead, going, another, goes, suddenly, emits, horrors, absorbs, sic, 08388, jersey, qed, strange, feynman, reference, constants, codata, bransden, joachain, longman, 1983, 44401, 722, 1940phrv, 716p, phys, rev, official, website, cern, sir, courier, hardy, lucien, 1996, contextuality, boston, 481, 4698, 015, 8715, 0_4, appraisal, bliokh, konstantin, punzmann, horst, xia, hua, nori, franco, shats, michael, january, eabm1295, 35061526, 8782445, pmc, 1126, sciadv, abm1295, 2022scia, 1295b, advances, 1986, 505, 14580, 1986amjph, 500o, 500, schroeder, 1995, advanced, program, peskin, lorcé, cédric, august, controversy, 248, physrep, 010, 2014phr, 163l, 1309, 4235, 163, reports, fröhlich, jürg, 2009, duplantier, bertrand, raimond, jean, michel, rivasseau, vincent, eds, birkhäuser, 8798, 8799, 0_1, 0801, 2724, progress, giulini, domenico, 578, 11858, 001m, 0000, 0013, 13c8, hdl, 005, 2008shpmp, 557g, 0710, 3128, 557, lincoln, don, fermilab, sebens, charles, 007, 2019shpmp, 40s, 1806, 01121, 273, 272, 373, 88702, 372, merzbacher, eugen, yrast, isomers, flip, engineering, lubanski, pseudovector, kramers, holstein, primakoff, helicity, dynamic, chirality, evidence, 1922, assumed, isotropic, year, phipps, again, peaks, once, closed, shells, unmatched, outer, responds, bellamy, taylor, 1928, proved, formalized, invented, pioneered, fortunately, managed, resolve, unpublished, difference, convinced, insist, invalid, 385, llewellyn, unconvinced, pursue, him, formulate, stating, autumn, came, dutch, advice, young, regretted, publication, pointed, problems, spinning, hendrik, leiden, samuel, unknown, assistants, heard, criticized, severely, noting, hypothetical, surface, moving, faster, rotate, quickly, enough, violate, largely, criticism, decided, publish, alfred, landé, ralph, 1910, relationships, involving, partially, summarized, transitions, obeyed, correlated, 1924, empirical, propose, introducing, outermost, shell, zeeman, selection, 106, alkali, metals, emission, lecturing, manifestations, indirect, emerging, application, binary, carrier, metal, doped, imparts, potential, facilitate, fabrication, efficient, zno, dilute, semiconductor, materials, transistor, played, development, verification, second, clocks, coupling, plays, computer, memories, radio, medical, gmr, drive, head, hard, disks, giant, magnetoresistive, mri, medicine, proton, implications, practical, collisions, collision, decay, supplemented, conclusion, pion, ray, detailed, balance, sophisticated, improvements, monochromatic, split, passed, selected, separated, found, tables, followed, refers, unchanged, negated, column, 209, longest, lived, isotope, entry, bismuth, citation, tractable, multiparticle, consist, fold, generalization, indices, forms, repeatedly, construct, dimensions, calculated, arbitrarily, yields, separable, singlet, triplet, lie, algebras, incompatible, mixture, chance, regardless, prior, commute, diagonalizing, termed, normalizing, length, unity, works, except, 2u_, iu_, generalizes, dot, easily, let, unit, correspondingly, eigenstate, provided, collapses, designed, represented, postulates, still, overall, imaginary, present, software, textbooks, prefer, sympy, hermitian, find, construction, associate, according, antisymmetric, parametrizing, bar, tfrac, omega, try, determine, discover, major, obstacle, faithful, recalling, written, identity, picks, minus, crucial, furnished, full, im2, equiv, built, compounding, angles, commutators, evaluate, expected, relied, 164, working, speaking, furnish, covering, plane, normal, parameters, depend, trivially, linear, represent, associating, preserve, inner, convenient, satisfying, prefactor, reduce, permutation, postulate, daily, life, interchanges, wavefunction, cartesian, observables, distinguishes, conserved, processes, say, reason, exclude, spherical, harmonics, raising, lowering, follows, expressed, kets, levi, civita, symbol, varepsilon, label, characterized, labels, poincaré, said, objects, differences, detectable, return, exact, needs, 720, analogies, straight, stick, sphere, whatever, turned, möbius, strip, plate, trick, handy, easy, exhibit, phenomena, exert, putting, undergoes, gyroscope, phenomenon, behaviour, gyroscopic, think, whose, describe, turns, very, simultaneous, statistically, collections, placed, pure, specifies, achieve, maximum, 100, every, drops, off, smoothly, increases, until, detectors, reaches, minimum, apparatus, correspond, respectively, baryon, previous, conventionally, fast, contains, hand, without, electric, significantly, independent, larger, unnatural, via, corrections, active, area, research, put, tuning, scale, magneton, approx, minimally, extended, predicts, indication, motions, triumphs, prediction, parentheses, denoting, connecting, surrounding, virtual, 002, 304, nonzero, exclusively, assuming, spheres, several, ways, deflection, themselves, schematic, depicting, black, arrow, upward, center, downward, splits, groups, specifically, carries, ability, aligns, individually, act, received, considerable, treatment, within, respective, mainstream, theoreticians, predicted, explaining, proven, breaking, graviton, pairs, superconductivity, liquid, superfluid, laser, weak, gluon, carrying, forces, common, compaction, sometimes, resist, overly, close, degeneracy, profound, roles, distinction, simultaneously, roughly, restriction, bunch, together, behaves, broadly, conventional, altered, numbered, differs, nonconductive, object, distributions, differing, laws, specific, derivative, over, true, ambiguous, might, decide, term, aspect, extends, arising, solution, rather, nearly, nevertheless, appears, treated, interpreted, partial, conjugate, implies, parallel, name, suggests, originally, conceived, orbits, survived, fundamentally, alters, understood, differently, depending, definitive, trajectories, driven, wavefield, continuous, allow, transfer, occurs, fixed, few, purposes, ignored, rigid, word, suggest, computed, applying, calculating, essentially, circulating, flow, subwavelength, circular, frederik, belinfante, central, figure, rejected, explain, later, insisted, considering, develop, insistence, style, initiated, era, dominate, concrete, secondary, optional, earliest, fails, examined
Text of the page (random words):
mathbf n e i frac theta 2 hat mathbf n cdot boldsymbol sigma i cos frac theta 2 i left hat mathbf n cdot boldsymbol sigma right sin frac theta 2 for higher spins is tractable but less simple 31 parity edit main article parity physics in tables of the spin quantum number s for nuclei or particles the spin is often followed by a or citation needed this refers to the parity with for even parity wave function unchanged by spatial inversion and for odd parity wave function negated by spatial inversion for example see the isotopes of bismuth in which the list of isotopes includes the column nuclear spin and parity for bi 209 the longest lived isotope the entry 9 2 means that the nuclear spin is 9 2 and the parity is odd measuring spin edit the nuclear spin of atoms can be determined by sophisticated improvements to the original stern gerlach experiment 32 a single energy monochromatic molecular beam of atoms in an inhomogeneous magnetic field will split into beams representing each possible spin quantum state for an atom with electronic spin s and nuclear spin i there are 2 s 1 2 i 1 spin states for example neutral na atoms which have s 1 2 were passed through a series of inhomogeneous magnetic fields that selected one of the two electronic spin states and separated the nuclear spin states from which four beams were observed thus the nuclear spin for 23 na atoms was found to be i 3 2 33 34 the spin of pions a type of elementary particle was determined by the principle of detailed balance applied to those collisions of protons that produced charged pions and deuterium p p π d displaystyle p p rightarrow pi d the known spin values for protons and deuterium allows analysis of the collision cross section to show that π displaystyle pi has spin s π 0 displaystyle s_ pi 0 a different approach is needed for neutral pions in that case the decay produced two gamma ray photons with spin one π 0 2 γ displaystyle pi 0 rightarrow 2 gamma this result supplemented with additional analysis leads to the conclusion that the neutral pion also has spin zero 35 66 applications edit spin has important theoretical implications and practical applications well established direct applications of spin include nuclear magnetic resonance nmr spectroscopy in chemistry electron spin resonance esr or epr spectroscopy in chemistry and physics magnetic resonance imaging mri in medicine a type of applied nmr which relies on proton spin density giant magnetoresistive gmr drive head technology in modern hard disks electron spin plays an important role in magnetism with applications for instance in computer memories the manipulation of nuclear spin by radio frequency waves nuclear magnetic resonance is important in chemical spectroscopy and medical imaging spin orbit coupling leads to the fine structure of atomic spectra which is used in atomic clocks and in the modern definition of the second precise measurements of the g factor of the electron have played an important role in the development and verification of quantum electrodynamics photon spin is associated with the polarization of light photon polarization an emerging application of spin is as a binary information carrier in spin transistors the original concept proposed in 1990 is known as datta das spin transistor 36 electronics based on spin transistors are referred to as spintronics the manipulation of spin in dilute magnetic semiconductor materials such as metal doped zno or tio 2 imparts a further degree of freedom and has the potential to facilitate the fabrication of more efficient electronics 37 there are many indirect applications and manifestations of spin and the associated pauli exclusion principle starting with the periodic table of chemistry history edit see also history of quantum mechanics wolfgang pauli lecturing spin was first discovered in the context of the emission spectrum of alkali metals starting around 1910 many experiments on different atoms produced a collection of relationships involving quantum numbers for atomic energy levels partially summarized in bohr s model for the atom 38 106 transitions between levels obeyed selection rules and the rules were known to be correlated with even or odd atomic number additional information was known from changes to atomic spectra observed in strong magnetic fields known as the zeeman effect in 1924 wolfgang pauli used this large collection of empirical observations to propose a new degree of freedom 7 introducing what he called a two valuedness not describable classically 39 associated with the electron in the outermost shell the physical interpretation of pauli s degree of freedom was initially unknown ralph kronig one of alfred 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 40 in the autumn of 1925 the same thought came to dutch physicists george uhlenbeck and samuel goudsmit at leiden university under the advice of paul ehrenfest they published their results 41 the young physicists immediately regretted the publication hendrik lorentz and werner heisenberg both pointed out problems with the concept of a spinning electron 42 pauli was especially unconvinced and continued to pursue his two valued degree of freedom this allowed him to formulate the pauli exclusion principle stating that no two electrons can have the same quantum state in the same quantum system fortunately by february 1926 llewellyn thomas managed to resolve a factor of two discrepancy between experimental results for the fine structure in the hydrogen spectrum and calculations based on uhlenbeck and goudsmit s and kronig s unpublished model 2 385 this discrepancy was due to a relativistic effect the difference between the electron s rotating rest frame and the nuclear rest frame the effect is now known as thomas precession 7 thomas result convinced pauli that electron spin was the correct interpretation of his two valued degree of freedom while he continued to insist that the classical rotating charge model is invalid 39 6 in 1927 pauli formalized the theory of spin using the theory of quantum mechanics invented by erwin schrödinger and werner heisenberg he pioneered the use of pauli matrices as a representation of the spin operators and introduced a two component spinor wave function pauli s theory of spin was non relativistic in 1928 paul dirac published his relativistic electron equation using a four component spinor known as a dirac spinor for the electron wave function in 1940 pauli proved the spin statistics theorem which states that fermions have half integer spin and bosons have integer spin 7 in retrospect the first direct experimental evidence of the electron spin was the stern gerlach experiment of 1922 however the correct explanation of this experiment was only given in 1927 43 the original interpretation assumed the two spots observed in the experiment were due to quantized orbital angular momentum however in 1927 ronald g j fraser de showed that sodium atoms are isotropic with no orbital angular momentum and suggested that the observed magnetic properties were due to electron spin 44 in the same year thomas erwin phipps and john bellamy taylor de applied the stern gerlach technique to hydrogen atoms the ground state of hydrogen has zero angular momentum but the measurements again showed two peaks 45 once the quantum theory became established it became clear that the original interpretation could not have been correct the possible values of orbital angular momentum along one axis is always an odd number unlike the observations hydrogen atoms have a single electron with two spin states giving the two spots observed silver atoms have closed shells which do not contribute to the magnetic moment and only the unmatched outer electron s spin responds to the field see also edit chirality physics dynamic nuclear polarization helicity particle physics holstein primakoff transformation kramers theorem pauli equation pauli lubanski pseudovector rarita schwinger equation representation theory of su 2 spin angular momentum of light spin engineering spin flip spin isomers of hydrogen spin orbit interaction spin tensor spintronics spin wave yrast references edit merzbacher eugen 1998 quantum mechanics 3rd ed john wiley sons pp 372 373 isbn 978 0 471 88702 7 1 2 3 4 5 griffiths david 2005 introduction to quantum mechanics 2nd ed eisberg robert resnick robert 1985 quantum physics of atoms molecules solids nuclei and particles 2nd ed wiley pp 272 273 isbn 978 0 471 87373 0 1 2 sebens charles t november 2019 how electrons spin studies in history and philosophy of science part b studies in history and philosophy of modern physics 68 40 50 arxiv 1806 01121 bibcode 2019shpmp 68 40s doi 10 1016 j shpsb 2019 04 007 lincoln don what s the point fermilab today archived from the original on 2023 06 01 retrieved 2023 06 16 1 2 3 giulini domenico september 2008 electron spin or classically non describable two valuedness studies in history and philosophy of science part b studies in history and philosophy of modern physics 39 3 557 578 arxiv 0710 3128 bibcode 2008shpmp 39 557g doi 10 1016 j shpsb 2008 03 005 hdl 11858 00 001m 0000 0013 13c8 1 1 2 3 4 5 fröhlich jürg 2009 spin or actually spin and quantum statistics in duplantier bertrand raimond jean michel rivasseau vincent eds the spin progress in mathematical physics vol 55 basel birkhäuser basel pp 1 60 arxiv 0801 2724 doi 10 1007 978 3 7643 8799 0_1 isbn 978 3 7643 8798 3 leader elliot lorcé cédric august 2014 the angular momentum controversy what s it all about and does it matter physics reports 541 3 163 248 arxiv 1309 4235 bibcode 2014phr 541 163l doi 10 1016 j physrep 2014 02 010 1 2 peskin m e schroeder d v 1995 quantum field theory the advanced book program ch 3 1 2 ohanian hans c 1986 06 01 what is spin pdf american journal of physics 54 6 500 505 bibcode 1986amjph 54 500o doi 10 1119 1 14580 archived pdf from the original on 2024 09 07 retrieved 2023 06 15 bliokh konstantin y punzmann horst xia hua nori franco shats michael 21 january 2022 field theory spin and momentum in water waves science advances 8 3 eabm1295 bibcode 2022scia 8 1295b doi 10 1126 sciadv abm1295 pmc 8782445 pmid 35061526 hardy lucien 1996 contextuality in bohmian mechanics bohmian mechanics and quantum theory an appraisal boston studies in the philosophy of science vol 184 pp 67 76 doi 10 1007 978 94 015 8715 0_4 isbn 978 90 481 4698 7 whittaker edmund sir 1989 a history of the theories of aether and electricity vol 2 courier dover publications pp 87 131 isbn 0 486 26126 3 cite book cs1 maint multiple names authors list link information about higgs boson in cern s official website pauli wolfgang 1940 the connection between spin and statistics pdf phys rev 58 8 716 722 bibcode 1940phrv 58 716p doi 10 1103 physrev 58 716 archived pdf from the original on 2024 01 28 retrieved 2024 01 28 physics of atoms and molecules b h bransden c j joachain longman 1983 isbn 0 582 44401 2 2022 codata value electron g factor the nist reference on constants units and uncertainty nist may 2024 retrieved 2024 05 18 feynman r p 1985 electrons and their interactions qed the strange theory of light and matter princeton new jersey princeton university press p 115 isbn 978 0 691 08388 9 after some years it was discovered that this value 1 2 g was not exactly 1 but slightly more something like 1 00116 this correction was worked out for the first time in 1948 by schwinger as j j divided by 2 π sic where j is the square root of the fine structure constant and was due to an alternative way the electron can go from place to place instead of going directly from one point to another the electron goes along for a while and suddenly emits a photon then horrors it absorbs its own photon marciano w j sanda a i 1977 exotic decays of the muon and heavy leptons in gauge theories physics letters b67 3 303 305 bibcode 1977phlb 67 303m doi 10 1016 0370 2693 77 90377 x lee benjamin w shrock robert e september 1977 natural suppression of symmetry violation in gauge theories muon and electron lepton number nonconservation physical review d 16 5 1444 1473 bibcode 1977phrvd 16 1444l doi 10 1103 physrevd 16 1444 k fujikawa r e shrock 1980 magnetic moment of a massive neutrino and neutrino spin rotation physical review letters 45 12 963 966 bibcode 1980phrvl 45 963f doi 10 1103 physrevlett 45 963 bell nicole f cirigliano v ramsey musolf m j vogel p wise mark b 4 october 2005 how magnetic is the dirac neutrino physical review letters 95 15 151802 arxiv hep ph 0504134 bibcode 2005phrvl 95o1802b doi 10 1103 physrevlett 95 151802 pmid 16241715 quanta a handbook of concepts p w atkins oxford university press 1974 isbn 0 19 855493 1 tung wu ki 2020 8 4 1 group theory in physics an introduction to symmetry principles group representations and special functions in classical and quantum physics london england uk world scientific isbn 978 0 00098975 8 berestetskii vladimir b lifshitz evgeny m pitaevskii lev p 1982 quantum electrodynamics course of theoretical physics vol 4 2nd ed butterworth heinemann isbn 978 0 7506 3371 0 tung wu ki 2020 theorem 10 10 group theory in physics an introduction to symmetry principles group representations and special functions in classical and quantum physics london england uk world scientific isbn 978 0 00098975 8 weinberg steven 2005 the quantum theory of fields vol 1 cambridge university press isbn 978 0 521 67053 1 messiah albert 2014 angular momentum in quantum mechanics quantum mechanics mineola ny dover publications p 540 isbn 978 1 306 51279 4 oclc 874097814 hall brian c 2013 quantum theory for mathematicians graduate texts in mathematics vol 267 pp 354 358 bibcode 2013qtm book h doi 10 1007 978 1 4614 7116 5 isbn 978 1 4614 7115 8 sakurai jun john napolitano jim 2017 modern quantum mechanics pdf 2nd ed cambridge cambridge university press isbn 978 1 108 42241 3 curtright t l fairlie d b zachos c k 2014 a compact formula for rotations as spin matrix polynomials sigma 10 084 arxiv 1402 3541 bibcode 2014sigma 10 084c doi 10 3842 sigma 2014 084 hamilton donald r december 1941 molecular beams and nuclear moments american journal of physics 9 6 319 337 bibcode 1941amjph 9 319h doi 10 1119 1 1991712 rabi i i cohen v w april 1933 the nuclear spin of sodium physical review 43 7 582 583 bibcode 1933phrv 43 582r doi 10 1103 physrev 43 582 estermann i july 1946 molecular beam technique reviews of modern physics 18 3 300 323 bibcode 1946rvmp 18 300e doi 10 1103 revmodphys 18 300 perkins donald h 2008 introduction to high energy physics 4 aufl 8 print ed cambridge cambridge un...
|
