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Integral approximation method popular in condensed matter physics
A Sommerfeld expansion is an approximation method developed by Arnold Sommerfeld in 1928 for a certain class of integrals which are common in condensed
Sommerfeld_expansion
Atomic model introduced by Niels Bohr in 1913
enhancements to the Bohr model were proposed, most notably the Sommerfeld or Bohr–Sommerfeld models, which suggested that electrons travel in elliptical
Bohr_model
Model of electrons within a metallic solid
Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model
Free_electron_model
Sommerfeld was a German theoretical physicist whom the following is named after: Sommerfeld coefficient Sommerfeld constant (α) Sommerfeld expansion Sommerfeld
List of things named after Arnold Sommerfeld
List_of_things_named_after_Arnold_Sommerfeld
Dimensionless number that quantifies the strength of the electromagnetic interaction
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical
Fine-structure_constant
Measure of voltage induced by change of temperature
{\displaystyle E\approx \mu \pm k_{\rm {B}}T} , one can perform a Sommerfeld expansion c ( E ) = c ( μ ) + c ′ ( μ ) ( E − μ ) + O [ ( E − μ ) 2 ] {\displaystyle
Seebeck_coefficient
Ecuadorian foreign minister
María Gabriela Sommerfeld Rosero became the Ecuadorian foreign minister in 2023. She led tourism for Quito, and had been the CEO of multiple airlines and
Gabriela_Sommerfeld
Steam engine where steam is expanded in stages
Simmons-Boardman Publishing Corporation, 30 Church Street, New York p.813 Sommerfeld, Arnold (1950). Mechanics: Lectures on Theoretical Physics. Academic Press
Compound_steam_engine
Result used in the theory of propagation of waves
The Sommerfeld identity is a mathematical identity, due Arnold Sommerfeld, used in the theory of propagation of waves, e i k R R = ∫ 0 ∞ I 0 ( λ r ) e
Sommerfeld_identity
Outgoing spherical wave as a linear combination of plane waves
equation in layered media. The expansion also covers evanescent wave components. It is often preferred to the Sommerfeld identity when the field representation
Weyl_expansion
Physical model of non-interacting fermions
Fermi gas is related to the zero temperature Fermi energy EF by a Sommerfeld expansion (assuming k B T ≪ E F {\displaystyle k_{\rm {B}}T\ll E_{\mathrm {F}
Fermi_gas
Heat capacity of an electron gas
the development of quantum mechanics. This paradox was solved by Arnold Sommerfeld after the discovery of the Pauli exclusion principle, who recognised that
Electronic_specific_heat
Property of a thermodynamic system
constant temperature T H {\textstyle T_{\mathsf {H}}} during isothermal expansion stage and the heat Q C {\textstyle Q_{\mathsf {C}}} is transferred from
Entropy
Details in the emission spectrum of an atom
successful relativistic formula was given by Arnold Sommerfeld in 1916. In the same work, Sommerfeld also introduced the fine-structure constant. The gross
Fine_structure
German physicist (1901–1976)
München under Sommerfeld. In June 1922, Sommerfeld took Heisenberg to Göttingen to attend the Bohr Festival, because Sommerfeld had a sincere interest
Werner_Heisenberg
Unprotected cruiser of the German Imperial Navy
In 1920, she was sold, converted into a freighter, and renamed Adolf Sommerfeld. She served in this capacity for only three years, and was broken up for
SMS_Gefion
Early and High Middle Age German migration movement to the East
Medieval World, 500–1300: A Biographical Dictionary. Greenwood Press. Sommerfeld, Wilhelm von (2005) [1896]. Geschichte der Germanisierung des Herzogtums
Ostsiedlung
Religious denomination in South America
of whom nearly 15,000 were Old Colony Mennonites and 2,500 Bergthal or Sommerfeld Mennonites. In 1995, there were a total of 25 Mennonite colonies in Bolivia
Mennonites_in_Bolivia
Solution method for linear differential equations
(n+1/2)} . Either way, the condition on the energy is a version of the Bohr–Sommerfeld quantization condition, with a "Maslov correction" equal to 1/2. It is
WKB_approximation
Tabular arrangement of the chemical elements
those now known. They were improved further after the work of Arnold Sommerfeld and Edmund Stoner discovered more quantum numbers. The first one to systematically
Periodic_table
Spectral line splitting in electrical field
hydrogen atom and succeeded in observing splittings. By the use of the Bohr–Sommerfeld ("old") quantum theory, Paul Epstein and Karl Schwarzschild were independently
Stark_effect
Gas equation of state which accounts for non-ideal gas behavior
T_{\text{c}}} ). As Sommerfeld noted, "This is the case with air and with most other gases. Air can be cooled at will by repeated expansion and can finally
Van_der_Waals_equation
2024 American film
(2025) - Financial Information". The Numbers. Retrieved June 4, 2025. Sommerfeld, Seth (February 2, 2022). "Time travel rules get trippy in Tim Travers
Tim Travers and the Time Traveler's Paradox
Tim_Travers_and_the_Time_Traveler's_Paradox
German-born theoretical physicist (1879–1955)
that de Broglie waves could explain the quantization rules of Bohr and Sommerfeld. This paper would inspire Schrödinger's work of 1926. Einstein played
Albert_Einstein
Eigenvalue problem for the Laplace operator
expansion Blanche (2014). Helmholtz Equation, from the Encyclopedia of Mathematics. Noble (1958), pp. 27–29. Abramowitz & Stegun (1965). Sommerfeld (1949)
Helmholtz_equation
Former RAF station in East Sussex, England
Command with the intention of creating a fighter station as part of the expansion following the Battle of Britain. It was not laid out until 1943, by which
RAF_Chailey
"Secretary of State Marco Rubio and Ecuadorian Foreign Minister Gabriela Sommerfeld at a Joint Press Availability" (Press release). United States Department
List of international trips made by Marco Rubio as United States Secretary of State
List_of_international_trips_made_by_Marco_Rubio_as_United_States_Secretary_of_State
Language of ancient Sumer and Babylon
Cultures, Chicago, 159–184 Jagersma (2010: 9–10) Sallaberger (2023: 24) Sommerfeld, Walter. 2021. Old Akkadian. In: History of the Akkadian Language. Ed
Sumerian_language
cudende ratio per Nicolaum Coppernicum (1526), Erich Sommerfeld (trl.), published in: Erich Sommerfeld (ed.), Die Geldlehre des Nicolaus Copernicus: Texte
Prussian_estates
Epidemiological history book by William H. McNeill
McNeill's rejection of a New World origin for syphilis. Guns, Germs and Steel Sommerfeld, Johannes (2003). "Plagues and peoples revisited". EMBO Reports. 4 (suppl
Plagues_and_Peoples
Near-field diffraction
correspond well to the values calculated for them. According to the Rayleigh–Sommerfeld diffraction theory, the electric-field diffraction pattern at a point
Fresnel_diffraction
Property of physical systems that stays somewhat constant through slow changes
its classical adiabatic invariant. This determined the form of the Bohr–Sommerfeld quantization rule: the quantum number is the area in phase space of the
Adiabatic_invariant
Multivalued function in mathematics
by the Lambert W function. The first solution to this problem, due to Sommerfeld circa 1898, already contained an iterative method to determine the value
Lambert_W_function
French physicist (1892–1987)
Stoner. Another result was the elucidation of the insufficiency of the Sommerfeld formula for determining the position of lines in X-ray spectra; this discrepancy
Louis_de_Broglie
Physical law for definition of temperature
non-matter-transferring contact equilibrium between thermodynamic systems. According to Sommerfeld, Ralph H. Fowler coined the term zeroth law of thermodynamics while discussing
Zeroth_law_of_thermodynamics
Observational basis of thermodynamics
Thermodynamics, McGraw-Hill, London, ISBN 0-07-084057-1. Guggenheim (1985), p. 8. Sommerfeld, A. (1951/1955). Thermodynamics and Statistical Mechanics, vol. 5 of Lectures
Laws_of_thermodynamics
Development of linear transformations forming the Lorentz group
representations of the Lorentz transformations: Minkowski (1907–1908) and Sommerfeld (1909) used imaginary trigonometric functions, Frank (1909) and Varićak
History of Lorentz transformations
History_of_Lorentz_transformations
Wikimedia history article
hand over the route free of charge (and debt); the state offered the Sommerfeld Group land and construction costs for an extension to Krumme Lanke. The
History_of_the_Berlin_U-Bahn
Tool from special relativity
Minkowski spacetime by Albert Einstein (1907, 1912), Max Born (1909), Arnold Sommerfeld (1910), Max von Laue (1911), Hendrik Lorentz (1913), Friedrich Kottler
Rindler_coordinates
Computer program for antenna modeling
model buried radials or ground stakes. NEC-3 modified NEC-2 to include a Sommerfeld model to properly model wires buried in or close to the ground. NEC-4
Numerical Electromagnetics Code
Numerical_Electromagnetics_Code
c. 1300–750 BC archaeological culture of Central Europe
angle or at the base of the sickle body. The archaeologist Christoph Sommerfeld examined the rules and realized that the casting marks are composed of
Urnfield_culture
Propagation of information or matter faster than the speed of light
(1987). Optics (2nd ed.). Addison Wesley. p. 62. ISBN 978-0-201-11609-0. Sommerfeld, A. (1907). "An Objection Against the Theory of Relativity and its Removal"
Faster-than-light
Speed of electromagnetic waves
Simplistic calculations of the speed of distant galaxies due to the expansion of the universe appear to exceed the speed of light, but only local velocity
Speed_of_light
Mathematical model combining space and time
Annals of Physics (Annalen der Physik) was edited by Sommerfeld to remove this term. Sommerfeld also edited the published form of this lecture to revise
Spacetime
Physics concept expressed as E = mc²
approximated by neglecting "magnitudes of fourth and higher orders" of a series expansion. Einstein used a body emitting two light pulses in opposite directions
Mass–energy_equivalence
Indoor arena in Seattle, Washington, US
(PDF) from the original on October 21, 2021. Retrieved October 11, 2021. Sommerfeld, Seth (December 13, 2013). "Macklemore Caps 2013 With Seattle Blowout"
Climate_Pledge_Arena
High-proof liquor, generally made illicitly
Blumenthal, P; Steger, MC; Einfalt, D; Rieke-Zapp, J; Quintanilla Bellucci, A; Sommerfeld, K; Schwarz, S; Lachenmeier, DW (28 April 2021). "Methanol Mitigation
Moonshine
Theory of interwoven space and time by Albert Einstein
are active and ongoing areas in theoretical research. The early Bohr–Sommerfeld atomic model explained the fine structure of alkali metal atoms using
Special_relativity
Theoretical framework in physics
an electron is 1/2; the electron g-factor is 2; it led to the correct Sommerfeld formula for the fine structure of the hydrogen atom; and it could be used
Quantum_field_theory
Historically important optical effect
integral for the on-axis case (P1 is at the center of the shadow) as (see Sommerfeld): U ( P 1 ) = A e i k g g b b 2 + a 2 e i k b 2 + a 2 . {\displaystyle
Arago_spot
German Waffen-SS infantry division
brigade fought against a strong Soviet attack near Sommerfeld and destroyed a tank. After retaking Sommerfeld, the brigade and the 25th Panzer Division attacked
Dirlewanger_Brigade
City in Saxony, Germany
long-distance railway to go into operation in 1839, is also undergoing expansion for 200 km/h. The most important construction project in regional transport
Leipzig
Archaeological culture of Mesopotamia
from the Queen of Tilmun", in Barjamovic, G.; Dahl, J.L.; Koch, U.S.; Sommerfeld, W.; Goodnick-Westenholz, J. (eds.), Akkade is King: A collection of papers
Early Dynastic Period (Mesopotamia)
Early_Dynastic_Period_(Mesopotamia)
Second-order partial differential equation
radius a, the Green's function may be obtained by means of a reflection (Sommerfeld 1949): the source point P at distance ρ from the center of the sphere
Laplace's_equation
State of Mexico
States seemed imminent. On April 22, 1914, on the initiative of Felix A. Sommerfeld and Sherburne Hopkins, Pancho Villa traveled to Juárez to calm fears along
Chihuahua_(state)
Early proto-writing system
Millennium: Studies in Early Mesopotamia and Syria in Honor of Walter Sommerfeld and Manfred Krebernik (in French). Leiden: Brill. p. 299. Nissen 1997
Proto-cuneiform
Hexagonal lattice made of carbon atoms
graphene sheet in terms of a dyadic Green function (represented using Sommerfeld integrals) and exciting electric current. Even though these analytical
Graphene
German physicist and politician (1902–1980)
the guidance of mathematician David Hilbert and the physicist Arnold Sommerfeld. At Göttingen, Jordan became an assistant to the mathematician Richard
Pascual_Jordan
German physicist and astronomer
Störungstheorie. Advisor and reviewer: Alexander Wilkens. 2nd reviewer: Arnold Sommerfeld. Thüring – Biographical Note Friedenblitz Thüring – Biographical Note
Bruno_Thüring
Archipelago in Schleswig-Holstein, Germany
mechanics while on Heligoland in the 1920s. While a student of Arnold Sommerfeld at Munich, Heisenberg first met the Danish physicist Niels Bohr in 1922
Heligoland
Change in wavelength of light
breakthrough in the new science of cosmology: the universe had a history and its expansion could be investigated with physical models backed up with observational
Redshift
Problem in physics and astronomy
done by Wolfgang Pauli in 1921 in his doctoral dissertation under Arnold Sommerfeld, a study of the first ion of molecular hydrogen, namely the hydrogen molecular
Euler's_three-body_problem
American scientist and activist (1901–1994)
Fellowship to travel to Europe, to study under German physicist Arnold Sommerfeld in Munich, Danish physicist Niels Bohr in Copenhagen and Austrian physicist
Linus_Pauling
Town in Brandenburg, Germany
offences. In 2007, the verdict against former city councilor Reinhard Sommerfeld (Neuruppiner Initiative) was the only legally binding conviction of an
Neuruppin
Emission of electrons induced by an electrostatic field
currents were due to the emission of conduction electrons, only in 1927 did Sommerfeld argue that Fermi–Dirac statistics applied to the behavior of electrons
Field_electron_emission
Ancient Sumerian city
Mari Studies (ed. Gordon D. Young), Winona Lake, IN: Eisenbrauns, 1992 Sommerfeld, Walter (2021). "The 'Kish Civilization'". In Vita, Juan-Pablo (ed.).
Kish_(Sumer)
Global black market
Archived from the original on 27 October 2007. Retrieved 7 April 2008. Sommerfeld, Julia (February 2001). "Beating an addiction to meth". Meth's Deadly
Illegal_drug_trade
Origin and evolution of the symbols used to write equations and formulas
indices of coordinates, coefficients, or basis vectors. In 1917 Arnold Sommerfeld created the contour integral sign, and Dimitry Mirimanoff proposed the
History of mathematical notation
History_of_mathematical_notation
American physicist (1881–1948)
background was the old quantum theory of Max Planck, Niels Bohr and Arnold Sommerfeld. Tolman was elected to the American Philosophical Society in 1932. In
Richard_C._Tolman
Town in Warmian-Masurian Voivodeship, Poland
(1835–1911), astronomer Kurt Haehling (1893–1983), Wehrmacht general Martin Sommerfeld (1894–1939), Jewish emigre to the U.S. and university lecturer Herbert
Węgorzewo
Scientific phenomenon
redshifts (due to light exiting a gravitational field); and cosmological expansion (where space itself stretches). This article concerns itself only with
Relativistic_Doppler_effect
Particle Physics Arsenij Sokolov and Igor Ternov Sommerfeld–Kossel displacement law Spectroscopy Arnold Sommerfeld and Walther Kossel Stefan–Boltzmann law Thermodynamics
List of scientific laws named after people
List_of_scientific_laws_named_after_people
Quantum consistency equation
Proceedings of the 8th International Workshop on Mathematical Physics, Arnold Sommerfeld Institute, Clausthal, FRG, 1989, Springer-Verlag Berlin, ISBN 3-540-53503-9
Yang–Baxter_equation
Series of waves generated by distant weather systems
shear flows, U a ( y ) {\displaystyle Ua(y)} , based on the inviscid Orr-Sommerfeld equation. He found that the energy transfer from wind to water surface
Swell_(wave)
Chatty, Dawn (2009). Culture Summary: Bedouin. Human Relations Area Files. Sommerfeld, Walter (2021). "The "Kish Civilization"". In Vita, Juan-Pablo (ed.).
History_of_the_ancient_Levant
sky model Rayleigh–Sommerfeld diffraction theory Rayleigh wave equation Rayleigh waves Rayleigh's criterion Janzen–Rayleigh expansion Plateau–Rayleigh instability
List of things named after Lord Rayleigh
List_of_things_named_after_Lord_Rayleigh
French mathematician, physicist and engineer (1854–1912)
closed, orientable manifold Poincaré duality Poincaré disk model Poincaré expansion Poincaré gauge Poincaré group Poincaré half-plane model Poincaré homology
Henri_Poincaré
Tax policies in ancient Rome
Studies. 70: 101–125. doi:10.2307/299558. JSTOR 299558. S2CID 162507113. Sommerfeld, Ray M., Silvia A. Madeo, Kenneth E. Anderson, Betty R. Jackson (1992)
Taxation_in_ancient_Rome
Tunisian mathematician
equations (the linear theory is named here after Orr and Arnold Sommerfeld: Orr-Sommerfeld equations). He built on the work on a similar problem by Cédric
Nader_Masmoudi
City in Washington, United States
Dahlquist". South Whidbey Record. July 14, 2005. Retrieved February 10, 2022. Sommerfeld, Seth (November 17, 2015). "A Fiendish Conversation with Robert DeLong"
Bothell,_Washington
American physicist (born 1951)
2005 Mayent-Rothschild Visiting professor, Curie Institute, Paris 2006 Sommerfeld Lecturer, LMU Munich 2006 Lorentz Visiting Professor, Leiden University
David_Robert_Nelson
Relativistic wave equation in quantum mechanics
the expression for the energy levels for regular atoms, known as the Sommerfeld formula, is very similar. It is directly acquired from the above through
Klein–Gordon_equation
2011 Texas fire
Ridenour, Karen; Rissel, Sean; Powell, Wade; Gray, Rich; Fisher, Mike; Sommerfeld, Julie (May 2012). Bastrop Complex Wildfire Case Study (PDF) (Report)
Bastrop_County_Complex_Fire
relativity, Henri Poincaré (1905, 1906), Hermann Minkowski (1908), and Arnold Sommerfeld (1910) tried to modify Newton's theory and to establish a Lorentz invariant
History of gravitational theory
History_of_gravitational_theory
Economic occurrence
which the rate increases as the amount subject to taxation increases) Sommerfeld, Ray M., Silvia A. Madeo, Kenneth E. Anderson, Betty R. Jackson (1992)
Robin_Hood_effect
Former RAF station in Lincolnshire
Grass runway, orientated North-East/South-West (NE/SW). 2,400 ft x 50 ft Sommerfeld Tracking runway, numbered 13/31. 3,450 ft x 150 ft PSP (Pierced steel
RAF_Sutton_Bridge
Higher tax on richer sources
which the rate increases as the amount subject to taxation increases) Sommerfeld, Ray M.; Madeo, Silvia A.; Anderson, Kenneth E.; Jackson, Betty R. (1992)
Progressive_tax
Babylonian kings
Sassmannshausen (2000, pp. 409–424) Richardson (2007, pp. 25–26) Sommerfeld (1995a, pp. 920–922) Sommerfeld (1995b, pp. 467–490) Lafont (1998, pp. 575–577) Richardson
Kassite_dynasty
Numerical method in computational electromagnetics
transform of the spectral-domain Green's function, which is defined on the Sommerfeld integration path. Nevertheless, this integral cannot be evaluated analytically
Method of moments (electromagnetics)
Method_of_moments_(electromagnetics)
Investigations by Albert Einstein
In 1913, mathematician Otto Blumenthal, in collaboration with Arnold Sommerfeld, published an anthology of Einstein's papers with footnotes. For the equator–pole
Einstein's unsuccessful investigations
Einstein's_unsuccessful_investigations
Intermetallic compound with 4f and 5f electrons in unfilled electron bands
The proportionality constant γ {\displaystyle \gamma } is called the Sommerfeld coefficient. For electrons with a quadratic dispersion relation (as for
Heavy_fermion_material
Prussian officer (1850–1921)
Regiment No. 1" appointed him its honorary chairman. Boehn died at age 70 in Sommerfeld and was interred at the Invalids' Cemetery in Berlin. His burial place
Max_von_Boehn_(general)
Method for satisfying the Newtonian motion of a rigid body which consists of mass points
doi:10.1177/027836499101000406. hdl:2060/19900020578. S2CID 12166182. Sommerfeld, Arnold (1952). Lectures on Theoretical Physics, Vol. I: Mechanics. New
Constraint (computational chemistry)
Constraint_(computational_chemistry)
Architecture movement in (mainly German-speaking) Europe
secret Glass Chain group. The early works of the Bauhaus, such as the Sommerfeld House, were in this vein. Expressionism's dynamism and use of glass (whether
New Objectivity (architecture)
New_Objectivity_(architecture)
Subfamily of beetles
11646/zootaxa.4877.1.2. ISSN 1175-5334. PMID 33311325. S2CID 228840630. Andreas Sommerfeld; Werner Rammer; Marco Heurich; Torben Hilmers; Jörg Müller; Rupert Seidl
Bark_beetle
media is higher than the speed of light. This was investigated by Arnold Sommerfeld (1907, 1914) and Léon Brillouin (1914). They came to the conclusion that
Criticism of the theory of relativity
Criticism_of_the_theory_of_relativity
Hungarian-American mathematician (1893–1974)
Szeged under the supervision of Rudolf Ortvay, a former student of Arnold Sommerfeld. While Ortvay was not distinguished as a researcher, he was an inspirational
Cornelius_Lanczos
Musical by Jeff Bowen and Hunter Bell
(WERK7 theater, May and October 2022). For the Hamburg run, Benjamin Sommerfeld joined the cast as Hunter. In Munich, Robin Reitsma joined the cast as
Title_of_show
Defunct theory of electromagnetism
introduced four-vectors. Following Poincaré, also Minkowski (1908) and Arnold Sommerfeld (1910) tried to establish a Lorentz-invariant gravitational law. However
Lorentz_ether_theory
Branch of applied mathematics
early quantum physics followed by a heuristic framework devised by Arnold Sommerfeld (1868–1951) and Niels Bohr (1885–1962), but this was soon replaced by
Mathematical_physics
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