DOCSLIB.ORG

Erwin Schrödinger: a Compreensão Do Mundo Infinitesimal Através De Uma Realidade Ondulatória

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Erwin Schrödinger: a Compreensão Do Mundo Infinitesimal Através De Uma Realidade Ondulatória Douglas Guilherme Schmidt Erwin Schrödinger: a compreensão do mundo infinitesimal através de uma realidade ondulatória Mestrado em História da Ciência Pontifícia Universidade Católica de São Paulo São Paulo 2008 Douglas Guilherme Schmidt Erwin Schrödinger: a compreensão do mundo infinitesimal através de uma realidade ondulatória MESTRADO EM HISTÓRIA DA CIÊNCIA Dissertação apresentada à Banca Examinadora como exigência parcial para obtenção do título de Mestre em História da Ciência pela Pontifícia Universidade Católica de São Paulo, sob a orientação da Profa. Doutora Lilian Al-Chueyr Pereira Martins. Pontifícia Universidade Católica de São Paulo São Paulo 2008 SCHMIDT, Douglas Guilherme. “Erwin Schrödinger: a compreensão do mundo infinitesimal através de uma realidade ondulatória” São Paulo, 2008. Dissertação (Mestrado) – PUC-SP Programa: História da Ciência Orientadora: Profa. Dra. Lilian Al-Chueyr Pereira Martins Folha de aprovação Banca Examinadora _________________________________ _________________________________ _________________________________ Autorizo, exclusivamente para fins acadêmicos e científicos, a reprodução total ou parcial desta dissertação por processos fotocopiadores ou eletrônicos. Ass.: _____________________________________________________ Local e data: _______________________________________________ [email protected] A minha mãe Eliana, a minha esposa Maria Ângela e à memória de meu pai Guilherme. Agradecimentos À Professora e orientadora Lilian Al-Chueyr Pereira Martins por seu apoio e objetividade, elevando minha auto-estima e segurança na realização deste trabalho. Pela orientação do Professor Roberto de Andrade Martins que sabiamente me auxiliou durante a elaboração deste trabalho e que me autorizou a utilizar sua análise inédita dos trabalhos de Schrödinger de 1926. Aos Professores José Luiz Goldfarb e Roberto de Andrade Martins, que fizeram parte da minha banca de qualificação, dando sugestões importantes para melhoria desta dissertação. Pela orientação das Professoras Ana Maria Alfonso-Goldfarb e Maria Elice Brzezinski Prestes que me auxiliaram na elaboração do projeto de mestrado durante os primeiros passos do curso. Aos professores do programa pelo convívio, empenho e dedicação que tiveram neste breve espaço de tempo. Ao núcleo do programa bolsa-mestrado e oficina pedagógica da diretoria centro-sul da Secretaria da Educação do estado de São Paulo, pela dedicação e auxílio com relação à bolsa de estudos. A minha família, em especial, a minha esposa Maria Ângela que teve paciência e compreensão quando estive ausente. RESUMO O presente trabalho histórico investiga a fase inicial da construção da mecânica ondulatória formulada pelo físico austríaco Erwin Schrödinger (1887- 1961), dando especial atenção aos trabalhos por ele realizados de dezembro de 1925 até fevereiro de 1926. Nesse período, Schrödinger concebeu as bases de sua teoria quântica e redigiu os dois primeiros artigos sobre o assunto, publicados na revista Annalen der Physik. Esta dissertação analisa esses dois artigos, bem como alguns de seus precedentes e repercussões. É analisada em especial a influência da teoria de ondas de matéria do físico francês Louis de Broglie (1892- 1987) no desenvolvimento da teoria de Schrödinger, bem como outros trabalhos e circunstâncias importantes que contribuíram para a elaboração da mecânica ondulatória. Discute-se também a interpretação que o próprio Schrödinger deu à sua teoria, comparando-a com o enfoque adotado por outros físicos da época. Palavras chaves: Erwin Schrödinger, mecânica ondulatória, equação de onda de Schrödinger, quantização, função de onda, física quântica, mecânica quântica. ABSTRACT This historical research analyses the initial period of construction of wave mechanics, as propounded by the Austrian physicist Erwin Schrödinger (1887- 1961), emphasizing his work from December 1925 to February 1926. During these months Schrödinger created the basis of his quantum theory and wrote his two earlier papers on this subject. They were published in the Annalen der Physik. The present dissertation analyses those two papers, and some of their precedents and immediate consequences. Special attention is given to the influence of the theory of matter waves of the French physicist Louis de Broglie (1892-1987) upon the development of Schrödinger’s theory, as well as other works and relevant circumstances that contributed to the creation of wave mechanics. The dissertation also discusses the interpretation given by Schrödinger to his own theory, comparing it to the approach of other physicists of that time. Keywords: Erwin Schrödinger, wave mechanics, Schrödinger wave equation, quantization, wave function, quantum physics, quantum mechanics. SUMÁRIO INTRODUÇÃO – TEMÁTICA GERAL....................................................................................................... 1 CAPÍTULO 1 – A FÍSICA QUÂNTICA ANTES DA CONSTRUÇÃO DA MECÂNICA ONDULATÓRIA............................................................................................................................................. 6 1.1 PLANCK E A QUANTIZAÇÃO DA ENERGIA.......................................................................................... 6 1.2 ALBERT EINSTEIN E O QUANTUM DE LUZ .......................................................................................... 9 1.3 A TEORIA DOS CALORES ESPECÍFICOS DE EINSTEIN E O CONGRESSO SOLVAY................................ 12 1.4 O ÁTOMO QUANTIZADO DE NIELS BOHR........................................................................................ 14 1.5 A TEORIA RELATIVÍSTICA DE SOMMERFELD................................................................................... 16 1.6 O DESENVOLVIMENTO DA MECÂNICA MATRICIAL ........................................................................ 19 1.7 LOUIS DE BROGLIE E A NATUREZA DA LUZ..................................................................................... 21 1.8 AS ONDAS ASSOCIADAS ÀS PARTÍCULAS ........................................................................................ 22 1.9 EXPLICAÇÃO DA QUANTIZAÇÃO DO ÁTOMO, POR LOUIS DE BROGLIE.............................................. 24 1.10 LOUIS DE BROGLIE E A RELAÇÃO ENTRE ÓPTICA E MECÂNICA ..................................................... 27 1.11 A TEORIA FINAL DE LOUIS DE BROGLIE ....................................................................................... 29 CAPÍTULO 2 – SCHRÖDINGER E A TEORIA QUÂNTICA................................................................. 31 2.1 EINSTEIN E A TEORIA DE LOUIS DE BROGLIE.................................................................................. 32 2.2 SCHRÖDINGER E A ESTATÍSTICA DOS GASES................................................................................... 34 2.3 SCHRÖDINGER E A TESE DE LOUIS DE BROGLIE.............................................................................. 36 2.4 A BUSCA DE UMA EQUAÇÃO DE ONDA RELATIVÍSTICA ................................................................... 39 2.5 AS FÉRIAS DE SCHRÖDINGER NO NATAL DE 1925........................................................................... 43 2.6 O CADERNO DE ANOTAÇÕES DE SCHRÖDINGER ............................................................................. 47 2.7 O RETORNO A ZURICH E OS ARTIGOS DE 1926................................................................................ 48 CAPÍTULO 3. ANÁLISE DOS DOIS PRIMEIROS ARTIGOS DE SCHRÖDINGER DE 1926.......... 55 3.1 “QUANTIZAÇÃO COMO UM PROBLEMA DE AUTOVALOR. PRIMEIRA MEMÓRIA” .............................. 55 3.1.1 A estratégia de Schrödinger .................................................................................................. 55 3.1.2 Introdução da equação de onda ............................................................................................ 57 3.1.3 O átomo de hidrogênio.......................................................................................................... 59 3.1.4 As vibrações atômicas ........................................................................................................... 62 3.1.5 Energia e freqüência ............................................................................................................. 63 3.1.6 Batimentos e a condição de freqüência de Bohr ................................................................... 65 3.1.7 O adendo: outra apresentação da equação de onda............................................................. 66 3.2 “QUANTIZAÇÃO COMO UM PROBLEMA DE AUTOVALOR. SEGUNDA MEMÓRIA”.............................. 67 3.2.1 Justificativa da equação de onda .......................................................................................... 67 3.2.2 Hamilton e a relação entre óptica e mecânica...................................................................... 68 3.2.3 Coordenadas generalizadas e geometria não-euclidiana ..................................................... 70 3.2.4 A passagem à idéia de frente de onda ................................................................................... 73 3.2.5 Relação entre os princípios de Fermat e de Maupertuis....................................................... 76 3.2.6 Justificativa de uma “mecânica ondulatória”....................................................................... 77 3.2.7 As propriedades da onda de fase........................................................................................... 78 3.2.8 Grupos de ondas...................................................................................................................
Load more

Recommended publications
  • Shs-17-2018-14.Pdf
    Science beyond borders Nobukata Nagasawa ORCID 0000-0002-9658-7680 Emeritus Professor of University of Tokyo [email protected] On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics Abstract Possible reasons are studied why Ladislas (Władysław) Natanson’s paper on the statistical theory of radiation, published in 1911 both in English and in the German translation, was not cited properly in the early history of quantum statistics by outstanding scientists, such as Arnold Sommerfeld, Paul Ehrenfest, Satyendra Nath Bose and Albert Einstein. The social and psychological aspects are discussed as back- ground to many so far discussions on the academic evaluation of his theory. In order to avoid in the future such Natansonian cases of very limited reception of valuable scientific works, it is pro- posed to introduce a digital tag in which all the information of PUBLICATION e-ISSN 2543-702X INFO ISSN 2451-3202 DIAMOND OPEN ACCESS CITATION Nagasawa, Nobukata 2018: On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics. Studia Historiae Scientiarum 17, pp. 391–419. Available online: https://doi.org/10.4467/2543702XSHS.18.014.9334. ARCHIVE RECEIVED: 13.06.2017 LICENSE POLICY ACCEPTED: 12.09.2018 Green SHERPA / PUBLISHED ONLINE: 12.12.2018 RoMEO Colour WWW http://www.ejournals.eu/sj/index.php/SHS/; http://pau.krakow.pl/Studia-Historiae-Scientiarum/ Nobukata Nagasawa On social and psychological aspects of a negligible reception... relevant papers published so far should be automatically accu- mulated and updated.
    [Show full text]
  • On Max Born's Vorlesungen ¨Uber Atommechanik, Erster Band
    On Max Born’s Vorlesungen uber¨ Atommechanik, Erster Band Domenico Giulini Institute for Theoretical Physics, University of Hannover Appelstrasse 2, D-30167 Hannover, Germany and Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm 1, D-28359 Bremen, Germany. [email protected] Abstract A little more than half a year before Matrix Mechanics was born, Max Born finished his book Vorlesungen uber¨ Atommechanik, Erster Band, which is a state-of-the-art presentation of Bohr-Sommerfeld quantisation. This book, which today seems almost forgotten, is remarkable for its epistemological as well as technical aspects. Here I wish to highlight one aspect in each of these two categories, the first being concerned with the roleˆ of axiomatisation in the heuristics of physics, the second with the problem of quantisation proper be- fore Heisenberg and Schrodinger.¨ This paper is a contribution to the project History and Foundations of Quantum Physics of the Max Planck Institute for the History of Sciences in Berlin and will appear in the book Research and Pedagogy. The History of Quantum Physics through its Textbooks, edited by M. Badino and J. Navarro. Contents 1 Outline 2 2 Structure of the Book 3 3 Born’s pedagogy and the heuristic roleˆ of the deductive/axiomatic method 7 3.1 Sommerfeld versus Born . 7 3.2 A remarkable introduction . 10 4 On technical issues: What is quantisation? 13 5 Einstein’s view 20 6 Final comments 23 1 1 Outline Max Born’s monograph Vorlesungen uber¨ Atommechanik, Erster Band, was pub- lished in 1925 by Springer Verlag (Berlin) as volume II in the Series Struktur der Materie [3].
    [Show full text]
  • China and Albert Einstein
    China and Albert Einstein China and Albert Einstein the reception of the physicist and his theory in china 1917–1979 Danian Hu harvard university press Cambridge, Massachusetts London, England 2005 Copyright © 2005 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America Library of Congress Cataloging-in-Publication Data Hu, Danian, 1962– China and Albert Einstein : the reception of the physicist and his theory in China 1917–1979 / Danian Hu. p. cm. Includes bibliographical references and index. ISBN 0-674-01538-X (alk. paper) 1. Einstein, Albert, 1879–1955—Influence. 2. Einstein, Albert, 1879–1955—Travel—China. 3. Relativity (Physics) 4. China—History— May Fourth Movement, 1919. I. Title. QC16.E5H79 2005 530.11'0951—dc22 2004059690 To my mother and father and my wife Contents Acknowledgments ix Abbreviations xiii Prologue 1 1 Western Physics Comes to China 5 2 China Embraces the Theory of Relativity 47 3 Six Pioneers of Relativity 86 4 From Eminent Physicist to the “Poor Philosopher” 130 5 Einstein: A Hero Reborn from the Criticism 152 Epilogue 182 Notes 191 Index 247 Acknowledgments My interest in Albert Einstein began in 1979 when I was a student at Qinghua High School in Beijing. With the centennial anniversary of Einstein’s birth in that year, many commemorative publications ap- peared in China. One book, A Collection of Translated Papers in Com- memoration of Einstein, in particular deeply impressed me and kindled in me a passion to understand Einstein’s life and works. One of the two editors of the book was Professor Xu Liangying, with whom I had the good fortune of studying while a graduate student.
    [Show full text]
  • A Selected Bibliography of Publications By, and About, Niels Bohr
    A Selected Bibliography of Publications by, and about, Niels Bohr Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 09 June 2021 Version 1.308 Title word cross-reference + [VIR+08]. $1 [Duf46]. $1.00 [N.38, Bal39]. $105.95 [Dor79]. $11.95 [Bus20]. $12.00 [Kra07, Lan08]. $189 [Tan09]. $21.95 [Hub14]. $24.95 [RS07]. $29.95 [Gor17]. $32.00 [RS07]. $35.00 [Par06]. $47.50 [Kri91]. $6.95 [Sha67]. $61 [Kra16b]. $9 [Jam67]. − [VIR+08]. 238 [Tur46a, Tur46b]. ◦ [Fra55]. 2 [Som18]. β [Gau14]. c [Dar92d, Gam39]. G [Gam39]. h [Gam39]. q [Dar92d]. × [wB90]. -numbers [Dar92d]. /Hasse [KZN+88]. /Rath [GRE+01]. 0 [wB90, Hub14, Tur06]. 0-19-852049-2 [Ano93a, Red93, Seg93]. 0-19-853977-0 [Hub14]. 0-521-35366-1 [Kri91]. 0-674-01519-3 [Tur06]. 0-85224-458-4 [Hen86a]. 0-9672617-2-4 [Kra07, Lan08]. 1 2 1.5 [GRE+01]. 100-˚aret [BR+85]. 100th [BR+85, KRW05, Sch13, vM02]. 110th [Rub97a]. 121 [Boh87a]. 153 [MP97]. 16 [SE13]. 17 [Boh55a, KRBR62]. 175 [Bad83]. 18.11.1962 [Hei63a]. 1911 [Meh75]. 1915 [SE13]. 1915/16 [SE13, SE13]. 1918 [Boh21a]. 1920s [PP16]. 1922 [Boh22a]. 1923 [Ros18]. 1925 [Cla13, Bor13, Jan17, Sho13]. 1927 [Ano28]. 1929 [HEB+80, HvMW79, Pye81]. 1930 [Lin81, Whe81]. 1930/41 [Fer68, Fer71]. 1930s [Aas85b, Stu79]. 1933 [CCJ+34].
    [Show full text]
  • Gravitational Radiation in F(R) Gravity: a Geometric Approach
    Gravitational Radiation in f(R) Gravity: A Geometric Approach Adam Scott Kelleher A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics and Astronomy. Chapel Hill 2013 Approved by: Laura Mersini-Houghton Y. Jack Ng Charles Evans Dmitri Khveshchenko Ryan Rohm Hugon Karvovski Abstract ADAM SCOTT KELLEHER: Gravitational Radiation in f(R) Gravity: A Geometric Approach. (Under the direction of Laura Mersini-Houghton.) I summarize experimental and theoretical constraints on gravity theories. I explore metric f(R) gravity, and explore scalar field theory analogs. I present a different kind of mechanism to raise the effective scalar mass in f(R) gravity in environments with particular ranges of background scalar curvatures, and thus suppress scalar effects on solar system curvature scales, while allowing scalar effects at different curvature scales. I review the post-Newtonian and post-Minkowskian mathemat- ical machinery for General Relativity, and generalize these expansions to metric f(R) gravity up to second order in small parameters. ii Dedicated to Bill Walsh, a true brother. iii Acknowledgments I would like to thank my brother for his support, Bart Dunlap and Greg Herschlag for useful conversations, and my advisor Laura Mersini-Houghton for her guidance. I thank the Department of Physics and Astronomy at UNC Chapel Hill for supporting this work. iv Table of Contents List of Figures ........................................... viii List of Abbreviations and Symbols .............................. ix 1 Introduction .......................................... 1 2 Properties of Gravity Theories .............................. 4 2.1 Equivalence Principles .
    [Show full text]
  • Quantization Conditions, 1900–1927
    Quantization Conditions, 1900–1927 Anthony Duncan and Michel Janssen March 9, 2020 1 Overview We trace the evolution of quantization conditions from Max Planck’s intro- duction of a new fundamental constant (h) in his treatment of blackbody radiation in 1900 to Werner Heisenberg’s interpretation of the commutation relations of modern quantum mechanics in terms of his uncertainty principle in 1927. In the most general sense, quantum conditions are relations between classical theory and quantum theory that enable us to construct a quantum theory from a classical theory. We can distinguish two stages in the use of such conditions. In the first stage, the idea was to take classical mechanics and modify it with an additional quantum structure. This was done by cut- ting up classical phase space. This idea first arose in the period 1900–1910 in the context of new theories for black-body radiation and specific heats that involved the statistics of large collections of simple harmonic oscillators. In this context, the structure added to classical phase space was used to select equiprobable states in phase space. With the arrival of Bohr’s model of the atom in 1913, the main focus in the development of quantum theory shifted from the statistics of large numbers of oscillators or modes of the electro- magnetic field to the detailed structure of individual atoms and molecules and the spectra they produce. In that context, the additional structure of phase space was used to select a discrete subset of classically possible motions. In the second stage, after the transition to modern quantum quan- tum mechanics in 1925–1926, quantum theory was completely divorced from its classical substratum and quantum conditions became a means of con- trolling the symbolic translation of classical relations into relations between quantum-theoretical quantities, represented by matrices or operators and no longer referring to orbits in classical phase space.1 More specifically, the development we trace in this essay can be summa- rized as follows.
    [Show full text]
  • Old Quantization, Angular Momentum, and Nonanalytic Problems
    September 3, 2020 Old Quantization, Angular Momentum, and Nonanalytic Problems Nelia Mann,1 Jessica Matli,1 and Tuan Pham2 1Union College, Physics and Astronomy Department, Schenectady, New York 12308, USA 2University of Wisconsin at Madison, Physics Department, Madison, Wisconsin 53706, USA We explore the method of old quantization as applied to states with nonzero angular momentum, and show that it leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We begin by reviewing the traditional application of this model to hydrogen, and discuss the way Einstein-Brillouin-Keller quantization resolves a mismatch be- tween old quantization states and true quantum mechanical states. We then analyze systems with logarithmic and Yukawa potentials, and compare the results of old quantization to those from solv- ing Schr¨odinger'sequation. We show that the old quantization techniques provide insight into the spread of energy levels associated with a given principal quantum number, as well as giving quan- titatively accurate approximations for the energies. Analyzing systems in this manner involves an educationally valuable synthesis of multiple numerical methods, as well as providing deeper insight into the connections between classical and quantum mechanical physics. PACS numbers: I. INTRODUCTION The origins of quantum mechanics are usually dated to 1905, with the publication of Einstein's work on the photoelectric effect [1], even though the study of Schr¨odinger'sequation and matrix mechanics|what we usually think of as quantum mechanics|was developed primarily in the mid-1920s [2, 3]. During the intervening two decades, quantum mechanics consisted of a series of ad hoc techniques that combined classical reasoning with simple rules for quantization.
    [Show full text]
  • Could the Inertia and Energy Content of Matter Diminish Over Cosmological Time?[1]
    International Journal of Theoretical and Mathematical Physics 2014, 4(3): 120-133 DOI: 10.5923/j.ijtmp.20140403.08 Could the Inertia and Energy Content of Matter Diminish [1] over Cosmological Time? John Kulick University of Connecticut, Connecticut, USA Abstract If the inertial properties of matter diminished according to Mi = T^(-1/3), with a corresponding loss of intrinsic energy, (The “_” notation represents a ratio of past measures over present measures so T represents the ratio of the objects location in Cosmological Time divided by the Age of the Universe, and Mi represents a ratio of the past over the present measures of inertial mass), then some interesting relationships result and a number of fundamental ambiguities in physics are resolved. Mentioning just one ambiguity; a gram of matter and a gram of radiant energy in intergalactic space now would maintain their equivalency over time, even though the photon loses energy as evidenced by the Cosmological Red Shift. As inertial mass is lost, relationships defined by a balance between inertial and spatial forces contract. (Spatial Forces are defined by spatial field based relationships associated with Gravity and Electromagnetism.) Spectra emitted or absorbed in the past would be “redder” than spectra produced in the present due to the denser atomic electrostatic field relationships in the present compared to the past. The contraction of atomic relationships also contracts local rulers which results in a measured Cosmological Red Shift that varies by λcosmological = T^(-2/3). This establishes an alternative or additional explanation for the observed Recessional Red shift. Clock rates established by a balance between inertial and spatial forces speed up over time so intervals of time to vary by, TΔ = T^(-2/3), which also produces an alternative or additional explanation for Time Dilation.
    [Show full text]
  • Harwit M. in Search of the True Universe.. the Tools, Shaping, And
    In Search of the True Universe Astrophysicist and scholar Martin Harwit examines how our understanding of the Cosmos advanced rapidly during the twentieth century and identifies the factors contributing to this progress. Astronomy, whose tools were largely imported from physics and engineering, benefited mid-century from the U.S. policy of coupling basic research with practical national priorities. This strategy, initially developed for military and industrial purposes, provided astronomy with powerful tools yielding access – at virtually no cost – to radio, infrared, X-ray, and gamma-ray observations. Today, astronomers are investigating the new frontiers of dark matter and dark energy, critical to understanding the Cosmos but of indeterminate socio-economic promise. Harwit addresses these current challenges in view of competing national priorities and proposes alternative new approaches in search of the true Universe. This is an engaging read for astrophysicists, policy makers, historians, and sociologists of science looking to learn and apply lessons from the past in gaining deeper cosmological insight. MARTIN HARWIT is an astrophysicist at the Center for Radiophysics and Space Research and Professor Emeritus of Astronomy at Cornell University. For many years he also served as Director of the National Air and Space Museum in Washington, D.C. For much of his astrophysical career he built instruments and made pioneering observations in infrared astronomy. His advanced textbook, Astrophysical Concepts, has taught several generations of astronomers through its four editions. Harwit has had an abiding interest in how science advances or is constrained by factors beyond the control of scientists. His book Cosmic Discovery first raised these questions.
    [Show full text]
  • The Divergent Histories of Bose-Einstein Statistics and the Forgotten Achievements of Władysław Natanson (1864–1937)
    Science Beyond Borders Michał Kokowski ORCID 0000-0002-5389-9051 L. and A. Birkenmajer Institute for the History of Science, Polish Academy of Sciences (Warsaw – Kraków, Poland) [email protected] The divergent histories of Bose-Einstein statistics and the forgotten achievements of Władysław Natanson (1864–1937) Abstract This article investigates the forgotten achievements of Wła- dysław Natanson (1864–1937) related to the creation of Bose- -Einstein statistics. The introductory part of the article presents considerations regarding the methodology of history and the history of exact sciences, and then the divergent research perspectives that can be taken in the description of the history of Bose-Einstein sta- tistics, as well as the author’s integrated approach to this issue, which eliminates the disadvantages of these divergent views. This integrated approach is then used to describe the achievements of Władysław Natanson related to the creation of Bose-Einstein statistics. These achievements are presented against the background and in the context of discussions which – relatively sporadically – PUBLICATION e-ISSN 2543-702X INFO ISSN 2451-3202 DIAMOND OPEN ACCESS CITATION Kokowski, Michał 2019: The divergent histories of Bose-Einstein statistics and the forgotten achievements of Władysław Natanson (1864–1937). Studia Historiae Scientiarum 18, pp. 327–464. DOI: 10.4467/2543702XSHS.19.012.11018. ARCHIVE RECEIVED: 13.04.2019 LICENSE POLICY ACCEPTED: 17.09.2019 Green SHERPA / PUBLISHED ONLINE: 15.11.2019 RoMEO Colour WWW http://www.ejournals.eu/sj/index.php/SHS/; http://pau.krakow.pl/Studia-Historiae-Scientiarum/ Michał Kokowski The divergent histories of Bose-Einstein statistics and the forgotten achievements... took place among various groups of researchers: historians and philosophers of science, physicists, sociologists of scientific knowledge in the 20th and 21st centuries.
    [Show full text]
  • Analysis of the Jun Ishiwara's" the Universal Meaning of the Quantum
    Analysis of the Jun Ishiwara’s "The universal meaning of the quantum of action" Karla Pelogia Philosophisch - Historische Fakultät, Universität Stuttgart Keplerstr. 17, 70174 Stuttgart, Deutschland∗ Carlos Alexandre Brasil São Carlos Institute of Physics (IFSC), University of São Paulo (USP), PO Box 369, 13560-970 São Carlos, SP, Brazil† Here we present an analysis of the paper “Universelle Bedeutung des Wirkungsquantums” (The universal meaning of the quantum of action), published by Jun Ishiwara in German in the “Proceed- ings of Tokyo Mathematico-Physical Society 8 (1915) 106-116”. In his work, Ishiwara, established in the Sendai University, Japan, proposed - simultaneously with Arnold Sommerfeld, William Wilson and Niels Bohr in Europe - the phase-space-integral quantization, a rule that would be incorpo- rated into the old-quantum-theory formalism. The discussions and analysis render this paper fully accessible to undergraduate students of physics with elementary knowledge of quantum mechanics. arXiv:1708.04676v1 [physics.hist-ph] 10 Aug 2017 ∗ [email protected] † [email protected] 2 I. INTRODUCTION No theory defies our common sense as much as quantum mechanics (QM). Richard Feynman (1918-1988) said explicitly on his lecture "Probability and Uncertainty: The Quantum Mechanical View of Nature" [Feynman 1985] that nobody understands the theory, Mário Schenberg (1914-1990) said that QM is the most important scientific revolution of the history of humanity [Schenberg 1984] and the debates between Albert Einstein (1879-1955)
    [Show full text]
  • Arxiv:1605.08027V2 [Quant-Ph] 14 Jul 2016 Uniain R Hw Ndphi Nacsil Aho Fo Fashion Accessible an Courses
    Elliptical orbits in the phase-space quantization Leonardo Andreta de Castro Carlos Alexandre Brasil Reginaldo de Jesus Napolitano São Carlos Institute of Physics, University of São Paulo PO Box 369, 13560-970, São Carlos, SP, Brazil. Abstract The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods (i) direct integration, (ii) Som- merfeld’s original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses. arXiv:1605.08027v2 [quant-ph] 14 Jul 2016 1 I. INTRODUCTION Few expressions are more frustrating to the student than “it is easy to prove that” followed by a non-trivial result. On the one hand, when well employed, that is, when the steps necessary to reach the final result are a natural consequence of what was explained before, the expression improves the reader’s self-confidence by stimulating the use of creativity to fill the logical and mathematical gaps in finding the solution. On the other hand, its inadequate use can make the student lose too much time in a fruitless pursuit of misguided paths, leaving them eventually discouraged when a simple sentence or set of references could point them to the right direction. This article addresses the specific but recurrent inadequate usage of “it is easy to show that” in many quantum mechanics textbooks[1–6] when deriving the energy levels of a hydrogen-like atom.[6] The problem consists in solving an integral resulting from the phase- space quantization conditions[6–11] fundamental in the old quantum theory when the electronic orbits are allowed to be elliptical (as opposed to circular), thus allowing for non- zero radial component of the momentum.
    [Show full text]