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Arnold Sommerfeld in Einigen Zitaten Von Ihm Und Über Ihn1
K.-P. Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn Seite 1 Karl-Peter Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn1 Kurze biographische Bemerkungen Arnold Sommerfeld [* 5. Dezember 1868 in Königsberg, † 26. April 1951 in München] zählt neben Max Planck, Albert Einstein und Niels Bohr zu den Begründern der modernen theoretischen Physik. Durch die Ausarbeitung der Bohrschen Atomtheorie, als Lehrbuchautor (Atombau und Spektrallinien, Vorlesungen über theoretische Physik) und durch seine „Schule“ (zu der etwa die Nobelpreisträger Peter Debye, Wolfgang Pauli, Werner Heisenberg und Hans Bethe gehören) sorgte Sommerfeld wie kein anderer für die Verbreitung der modernen Physik.2 Je nach Auswahl könnte Sommerfeld [aber] nicht nur als theoretischer Physiker, sondern auch als Mathematiker, Techniker oder Wissenschaftsjournalist porträtiert werden.3 Als Schüler der Mathematiker Ferdinand von Lindemann, Adolf Hurwitz, David Hilbert und Felix Klein hatte sich Sommerfeld zunächst vor allem der Mathematik zugewandt (seine erste Professur: 1897 - 1900 für Mathematik an der Bergakademie Clausthal). Als Professor an der TH Aachen von 1900 - 1906 gewann er zunehmendes Interesse an der Technik. 1906 erhielt er den seit Jahren verwaisten Lehrstuhl für theoretische Physik in München, an dem er mit wenigen Unterbrechungen noch bis 1940 (und dann wieder ab 19464) unterrichtete. Im Gegensatz zur etablierten Experimen- talphysik war die theoretische Physik anfangs des 20. Jh. noch eine junge Disziplin. Sie wurde nun zu -
Sitzungsberichte Der Mathematisch- Physikalischen Klasse Der Bayerischen Akademie Der Wissenschaften München
ZOBODAT - www.zobodat.at Zoologisch-Botanische Datenbank/Zoological-Botanical Database Digitale Literatur/Digital Literature Zeitschrift/Journal: Sitzungsberichte der mathematisch- physikalischen Klasse der Bayerischen Akademie der Wissenschaften München Jahr/Year: 1986 Band/Volume: 1985 Autor(en)/Author(s): Biermann Ludwig F. B., Grigull Ulrich Artikel/Article: Fünfzig Jahre Kepler-Kommission 50 Jahre Kepler- Kommission 23-31 BAYERISCHE AKADEMIE DER WISSENSCHAFTEN MATHEMATISCH-NATURWISSENSCHAFTLICHE KLASSE SITZUNGSBERICHTE JAHRGANG 1985 MÜNCHEN 1986 VERLAG DER BAYERISCHEN AKADEMIE DER WISSENSCHAFTEN In Kommission bei der C.H. Beck’schen Verlagsbuchhandlung München 50 Jahre Kepler-Kommission Ludwig F. B. Biermannt und Ulrich Grigull Vorgetragen auf der Gedenkfeier der Kepler-Kommission am 15. Juli 1985 Die Aktivitäten der Bayerischen Akademie der Wissenschaften zur Herausgabe der Werke von Johannes Kepler haben ihren Ursprung darin, daß das Akademiemitglied Walther von Dyck (*1856 in Mün- chen) sich mit Kepler zu beschäftigen begann, vermutlich auf Anre- gung seines Freundes Oskar von Miller. Schon Anfang desjahrhun- derts war Walther von Dyck von Oskar von Miller um einen Vor- trag über Johannes Kepler gebeten worden und hatte bei den Vorbe- reitungen dazu festgcstcllt, daß ein großer Teil der Schriften Keplers in der einzigen damals existierenden Ausgabe der Gesammelten Wer- ke - welche der württcmbcrgische Gelehrte Christian Frisch zwi- schen 1858 und 1871 besorgt hatte - nicht berücksichtigt war. Wal- ther von Dyck begann, Keplers Manuskripte systematisch zu sam- meln; als erstes Ergebnis erschienen 1910 unter den Abhandlungen der mathematisch-naturwissenschaftlichen Klasse unserer Akademie zwei wieder aufgefundene Prognostika auf diejahre 1604 und 1624, die Walther von Dyck am 5. November 1910 der Klasse vorlegte und die auch noch im gleichen Jahr gedruckt wurden. -
Chapter 6 Free Electron Fermi Gas
理学院 物理系 沈嵘 Chapter 6 Free Electron Fermi Gas 6.1 Electron Gas Model and its Ground State 6.2 Thermal Properties of Electron Gas 6.3 Free Electrons in Electric Fields 6.4 Hall Effect 6.5 Thermal Conductivity of Metals 6.6 Failures of the free electron gas model 1 6.1 Electron Gas Model and its Ground State 6.1 Electron Gas Model and its Ground State I. Basic Assumptions of Electron Gas Model Metal: valence electrons → conduction electrons (moving freely) ü The simplest metals are the alkali metals—lithium, sodium, 2 potassium, cesium, and rubidium. 6.1 Electron Gas Model and its Ground State density of electrons: Zr n = N m A A where Z is # of conduction electrons per atom, A is relative atomic mass, rm is the density of mass in the metal. The spherical volume of each electron is, 1 3 1 V 4 3 æ 3 ö = = p rs rs = ç ÷ n N 3 è 4p nø Free electron gas model: Suppose, except the confining potential near surfaces of metals, conduction electrons are completely free. The conduction electrons thus behave just like gas atoms in an ideal gas --- free electron gas. 3 6.1 Electron Gas Model and its Ground State Basic Properties： ü Ignore interactions of electron-ion type (free electron approx.) ü And electron-eletron type (independent electron approx). Total energy are of kinetic type, ignore potential energy contribution. ü The classical theory had several conspicuous successes 4 6.1 Electron Gas Model and its Ground State Long Mean Free Path: ü From many types of experiments it is clear that a conduction electron in a metal can move freely in a straight path over many atomic distances. -
Section I.9. Free Groups, Free Products, and Generators and Relations
I.9. Free Groups, Free Products, and Generators and Relations 1 Section I.9. Free Groups, Free Products, and Generators and Relations Note. This section includes material covered in Fraleigh’s Sections VII.39 and VII.40. We define a free group on a set and show (in Theorem I.9.2) that this idea of “free” is consistent with the idea of “free on a set” in the setting of a concrete category (see Definition I.7.7). We also define generators and relations in a group presentation. Note. To define a free group F on a set X, we will first define “words” on the set, have a way to reduce these words, define a method of combining words (this com- bination will be the binary operation in the free group), and then give a reduction of the combined words. The free group will have the reduced words as its elements and the combination as the binary operation. If set X = ∅ then the free group on X is F = hei. Definition. Let X be a nonempty set. Define set X−1 to be disjoint from X such that |X| = |X−1|. Choose a bijection from X to X−1 and denote the image of x ∈ X as x−1. Introduce the symbol “1” (with X and X−1 not containing 1). A −1 word on X is a sequence (a1, a2,...) with ai ∈ X ∪ X ∪ {1} for i ∈ N such that for some n ∈ N we have ak = 1 for all k ≥ n. The sequence (1, 1,...) is the empty word which we will also sometimes denote as 1. -
5 X-Ray Crystallography
Introductory biophysics A. Y. 2016-17 5. X-ray crystallography and its applications to the structural problems of biology Edoardo Milotti Dipartimento di Fisica, Università di Trieste The interatomic distance in a metallic crystal can be roughly estimated as follows. Take, e.g., iron • density: 7.874 g/cm3 • atomic weight: 56 3 • molar volume: VM = 7.1 cm /mole then the interatomic distance is roughly VM d ≈ 3 ≈ 2.2nm N A Edoardo Milotti - Introductory biophysics - A.Y. 2016-17 The atomic lattice can be used a sort of diffraction grating for short-wavelength radiation, about 100 times shorter than visible light which is in the range 400-750 nm. Since hc 2·10−25 J m 1.24 eV µm E = ≈ ≈ γ λ λ λ 1 nm radiation corresponds to about 1 keV photon energy. Edoardo Milotti - Introductory biophysics - A.Y. 2016-17 !"#$%&'$(")* S#%/J&T&U2*#<.%&CKET3&VG$GG./"#%G3&W.%-$/; +(."J&AN&>,%()&CTDB3&S.%)(/3&X.1*&W.%-$/; Y#<.)&V%(Z.&(/&V=;1(21&(/&CTCL&[G#%&=(1&"(12#5.%;&#G&*=.& "(GG%$2*(#/&#G&\8%$;1&<;&2%;1*$)1] 9/(*($));&=.&1*:"(."&H(*=&^_/F*./3&$/"&*=./&H(*=&'$`&V)$/2I&(/& S.%)(/3&H=.%.&=.&=$<()(*$*."&(/&CTBD&H(*=&$&*=.1(1&[a<.% "(.& 9/*.%G.%./Z.%12=.(/:/F./ $/&,)$/,$%$)).)./ V)$**./[?& 7=./&=.&H#%I."&$*&*=.&9/1*(*:*.&#G&7=.#%.*(2$)&V=;1(213&=.$"."& <;&>%/#)"&Q#--.%G.)"3&:/*()&=.&H$1&$,,#(/*."&G:))&,%#G.11#%&$*& *=.&4/(5.%1(*;&#G&0%$/IG:%*&(/&CTCL3&H=./&=.&$)1#&%.2.(5."&=(1& Y#<.)&V%(Z.?& !"#$%"#&'()#**(&8 9/*%#":2*#%;&<(#,=;1(21&8 >?@?&ABCD8CE Arnold Sommerfeld (1868-1951) ... Four of Sommerfeld's doctoral students, Werner Heisenberg, Wolfgang Pauli, Peter Debye, and Hans Bethe went on to win Nobel Prizes, while others, most notably, Walter Heitler, Rudolf Peierls, Karl Bechert, Hermann Brück, Paul Peter Ewald, Eugene Feenberg, Herbert Fröhlich, Erwin Fues, Ernst Guillemin, Helmut Hönl, Ludwig Hopf, Adolf KratZer, Otto Laporte, Wilhelm LenZ, Karl Meissner, Rudolf Seeliger, Ernst C. -
Translation of Three Short Papers by Grete Hermann
Journal for General Philosophy of Science (2020) 51:615–619 https://doi.org/10.1007/s10838-020-09530-6 ARTICLE Translation of Three Short Papers by Grete Hermann Guido Bacciagaluppi1 Published online: 27 November 2020 © The Author(s) 2020 After a number of years of relative neglect, it is now becoming apparent that Grete Her- mann (1901–1984) was one of the most accomplished neo-Kantian philosophers of the last century—in part thanks to the recent publication of two volumes on and of her work, one in English (Crull and Bacciagaluppi 2017) and one in German (Herrmann 2019), both reviewed in this issue. The latter in particular contains Hermann’s entire output on modern physics and philosophy of science. Below I translate the three shortest papers by Hermann in that volume, which I intro- duce here. They provide quick but fascinating glimpses into some of Hermann’s ideas on philosophy of science, quantum mechanics and transcendental idealism. They are: from 1935 a book review of Popper’s Logik der Forschung (the original German edition of The Logic of Scientifc Discovery), from 1936 a comment on Schlick’s posthumously published talk ‘Quantentheorie und Erkennbarkeit der Natur’ (‘Quantum Theory and Knowability of Nature’) and from 1937 a short summary of Hermann’s ideas on the relation between Kant’s philosophy and modern physics (specifcally electrodynamics, the special and gen- eral theories of relativity and quantum mechanics) presented at the Congrès Descartes in Paris.1 1 Popper Review Popper had published Logik der Forschung in late 1934 (with the impressum of the fol- lowing year, Popper 1935). -
The Isotope Effect: Prediction, Discussion, and Discovery
1 The isotope effect: Prediction, discussion, and discovery Helge Kragh Centre for Science Studies, Department of Physics and Astronomy, Aarhus University, 8000 Aarhus, Denmark. ABSTRACT The precise position of a spectral line emitted by an atomic system depends on the mass of the atomic nucleus and is therefore different for isotopes belonging to the same element. The possible presence of an isotope effect followed from Bohr’s atomic theory of 1913, but it took several years before it was confirmed experimentally. Its early history involves the childhood not only of the quantum atom, but also of the concept of isotopy. Bohr’s prediction of the isotope effect was apparently at odds with early attempts to distinguish between isotopes by means of their optical spectra. However, in 1920 the effect was discovered in HCl molecules, which gave rise to a fruitful development in molecular spectroscopy. The first detection of an atomic isotope effect was no less important, as it was by this means that the heavy hydrogen isotope deuterium was discovered in 1932. The early development of isotope spectroscopy illustrates the complex relationship between theory and experiment, and is also instructive with regard to the concepts of prediction and discovery. Keywords: isotopes; spectroscopy; Bohr model; atomic theory; deuterium. 1. Introduction The wavelength of a spectral line arising from an excited atom or molecule depends slightly on the isotopic composition, hence on the mass, of the atomic system. The phenomenon is often called the “isotope effect,” although E-mail: [email protected]. 2 the name is also used in other meanings. -
The Chaning Face of Science and Technology in the Ehrensaal of The
PREPRINT 13 Lisa Kirch The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955 The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955 Deutsches Museum Preprint Edited by Deutsches Museum Issue 13 Lisa Kirch received her Ph. D. in art history (University of Texas at Austin, 2003) with a dissertation on the portraits of Elector Palatine Ottheinrich (1502–1559). In collaboration with Andreas Kühne (LMU) she has published articles on portraits of the Herschel family and on the presentation and conservation of modern art. Her publications on visual and material culture in early-modern Germany appear under Miriam Hall Kirch. She is Associate Professor in the Art Department of the University of North Alabama. Lisa Kirch The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955 Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet unter http://dnb.d-nb.de abrufbar. Lisa Kirch, “The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955” © 2017 of the present edition: MV-Wissenschaft MV-Wissenschaft is published by readbox publishing GmbH, Dortmund http://unipress.readbox.net/ © Deutsches Museum Verlag All rights reserved Editor: Dorothee Messerschmid Layout and Design: Jutta Esser Cover illustration: Draft of the Lilienthal glider, 1895 -
Inside the Camera Obscura – Optics and Art Under the Spell of the Projected Image
MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2007 PREPRINT 333 Wolfgang Lefèvre (ed.) Inside the Camera Obscura – Optics and Art under the Spell of the Projected Image TABLE OF CONTENTS PART I – INTRODUCING AN INSTRUMENT The Optical Camera Obscura I A Short Exposition Wolfgang Lefèvre 5 The Optical Camera Obscura II Images and Texts Collected and presented by Norma Wenczel 13 Projecting Nature in Early-Modern Europe Michael John Gorman 31 PART II – OPTICS Alhazen’s Optics in Europe: Some Notes on What It Said and What It Did Not Say Abdelhamid I. Sabra 53 Playing with Images in a Dark Room Kepler’s Ludi inside the Camera Obscura Sven Dupré 59 Images: Real and Virtual, Projected and Perceived, from Kepler to Dechales Alan E. Shapiro 75 “Res Aspectabilis Cujus Forma Luminis Beneficio per Foramen Transparet” – Simulachrum, Species, Forma, Imago: What was Transported by Light through the Pinhole? Isabelle Pantin 95 Clair & Distinct. Seventeenth-Century Conceptualizations of the Quality of Images Fokko Jan Dijksterhuis 105 PART III – LENSES AND MIRRORS The Optical Quality of Seventeenth-Century Lenses Giuseppe Molesini 117 The Camera Obscura and the Availibility of Seventeenth Century Optics – Some Notes and an Account of a Test Tiemen Cocquyt 129 Comments on 17th-Century Lenses and Projection Klaus Staubermann 141 PART IV – PAINTING The Camera Obscura as a Model of a New Concept of Mimesis in Seventeenth-Century Painting Carsten Wirth 149 Painting Technique in the Seventeenth Century in Holland and the Possible Use of the Camera Obscura by Vermeer Karin Groen 195 Neutron-Autoradiography of two Paintings by Jan Vermeer in the Gemäldegalerie Berlin Claudia Laurenze-Landsberg 211 Gerrit Dou and the Concave Mirror Philip Steadman 227 Imitation, Optics and Photography Some Gross Hypotheses Martin Kemp 243 List of Contributors 265 PART I INTRODUCING AN INSTRUMENT Figure 1: ‘Woman with a pearl necklace’ by Vermeer van Delft (c.1664). -
A History of Quantum Chemistry
1 Quantum Chemistry qua Physics: The Promises and Deadlocks of Using First Principles In the opening paragraph of his 1929 paper “ Quantum Mechanics of Many-Electron Systems, ” Paul Adrien Maurice Dirac announced that: The general theory of quantum mechanics is now almost complete, the imperfections that still remain being in connection with the exact fi tting in of the theory with relativity ideas. These give rise to diffi culties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reac- tions, in which it is, indeed, usually suffi ciently accurate if one neglects relativity variation of mass with velocity and assumes only Coulomb forces between the various electrons and atomic nuclei. The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the diffi culty is only that the exact applica- tion of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. (Dirac 1929, 714, emphasis ours) For most members of the community of physicists, it appeared that the solution of chemical problems amounted to no more than quantum-mechanical calculations. Physicists came under the spell of Dirac ’ s reductionist program, and quantum chem- istry came to be usually regarded as a success story of quantum mechanics. -
Jahrestagung Der Deutschen Mathematiker-Vereinigung Deutschen Der Jahrestagung Herausgegeben Von / Edited by by Edited / Von Herausgegeben
2015 of of of thethethe Hendrik Niehaus , in Hamburg, Germany Germany in Hamburg, in Hamburg, , , 2015 2015 2015 2015 & September 21 – 25 schen Mathematiker-Vereinigung 25. restagung der restagung bis Jahrestagung der Jahrestagung Deutschen Mathematiker-Vereinigung und Hansestadt Hamburg Freie 21. edited by / von herausgegeben Benedikt Löwe Annual Meeting Deutsche Mathematiker-Vereinigung Deutsche Mathematiker-Vereinigung September bis bis Hamburg, Hansestadt und Freie September September Hendrik Niehaus Hendrik Löwe Benedikt & 25. 21. 2015 Jahrestagung der Deutschen Mathematiker-Vereinigung Deutschen der Jahrestagung herausgegeben von / edited by by edited / von herausgegeben Programm Schedule Monday, 21 September 2015 Tuesday, 22 September 2015 Wednesday, 23 September 2015 Thursday, 24 September 2015 Friday, 25 September 2015 Jørgen Ellegaard Andersen Michael Eichmair Kathrin Bringmann Charles M. Elliott Minimal surfaces, isoperimetry, and non-negative Topological quantum fi eld theory 9.00 -10.00 Meromorphic Maass forms PDEs on evolving domains scalar curvature in asymptotically fl at manifolds in low dimensional topology Hörsaal A Hörsaal A Hörsaal A Hörsaal A 10.00 - 10.30 Coffee Break Coffee Break Coffee Break Coffee Break Minisymposia 1: Minisymposia 3: Minisymposia 5: Minisymposia 7: #1, #2, #4, #15, #17, #18, #2, #4, #6, #12, #15, #17, #3, #5, #6, #10, #12, #14, #3, #5, #7, #8, #9, #11, 10.30 - 12.30 #20, #27, #32, #35, #36, #20, #21, #22, #26, #27, #31, #16, #19, #22, #23, #24, #25, #14, #16, #19, #23, #24, #37, #39. #32, #34, #35, #36, #37. #26, #28, #31, #37, #38. #25, #29, #30, #33, #38. 12.30 - 14.00 Lunch Break Lunch Break Mittagsseminar Lunch Break Mathematik in Industrie Minisymposia 2: Minisymposia 4: und Gesellschaft Minisymposia 8: 14.00 - 15.00 #1, #2, #4, #13, #15, #17, #18, #2, #4, #10, #15, #17, #18, #20, #21, #3, #5, #7, #8, #9, #11, #14, #16, #20, #21, #27, #32, #35, #36. -
Technische Universität München 2 TUM – University of Excellence Contents
Technische Universität München 2 TUM – University of Excellence Contents TUM Research and Teaching TUM: A global brand 6 TUM Faculties 10 Interdisciplinary horizons 18 TUM University Foundation 20 TUM People Faces 22 Nobel Prize winners 30 Inventors and discoverers 31 Discovering talent, promoting talent, using talent 32 Alumni 34 TUM Excellence Research Centers 38 Cutting-edge research 52 Collaborative Research Centers Transregional Collaborative Research Centers 56 TUM Environment and Locations International 60 Munich – the business capital 62 Munich – Garching – Weihenstephan: TUM 3 64 Culture and leisure 68 Contacts 70 Imprint 72 TUM – University of Excellence 3 Scientific, entrepreneurial, international Ever since its inception in 1868, the Technische Universität München has borne out what, since the time of Humboldt, has epitomized the idea of the university – education and training as scientific objective – research as fascination, adventure, character building and societal culture. Eminent figures have studied, taught and conducted research here – Nobel Prize winners, inventors, entrepreneurs, representatives of public life But we can thank a strong community spirit that knows no boundaries between the generations and nurtures performance for its rise to become a world-class university The most visible proof of the strength of the TUM family is the rebuilding of our university from the ruins of a world war that had virtually destroyed it Today, around 26,000 young people study here – 23 percent of them from abroad – in the 13 faculties