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Hieronder vindt u een overzicht van de archieven die voor dit onderzoek gebruikt zijn. Er is ook een totaaloverzicht van alle correspondentie op de speciale correspondentie pagina. Deze correspondentie is eerst gesorteerd op archief en vervolgens alfabetisch op naam. Daarnaast is er op termijn een chronologisch overzicht van de gebruikte wetenschappelijke en persoonlijke correspondentie.
1. Museum Boerhaave Leiden
Archief van Paul Ehrenfest in Museum Boerhaave te Leiden.
Inventaris: B. Wheaton, Catalogue of the Paul Ehrenfest Archive at the Museum
Boerhaave Leiden (1977)
2. Niels Bohr Archief
Archief van Niels Bohr in het Niels Bohr Instituut te Kopenhagen.
3. Archive for the history of Quantum Physics
Archief voor de geschiedenis van de Quantum Fysica, o.a. in Kopenhagen
Inventaris: T.S. Kuhn, J.L. Heilbron, P. Forman en L. Allen, Sources for the
history of quantum physics (1967)
4. Huisbibliotheek Paul Ehrenfest
Boeken, artikelen, brieven etc. opgeslagen in kamer 364 van het Instituut Lorentz
te Leiden
5. Rijksarchief in Noordholland
Archief van Nederlandse wetenschappers, waaronder H.A. Lorentz, te Haarlem
De historie van Ehrenfest in Leiden
Geschiedenis van Einstein in Leiden
Informatie over Paul Ehrenfest
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By Olivier Darrigol
Page 79 – 284
The Correspondence Principle
Introduction
Darrigol werkt in dit hoofdstuk het correspondentie principe van Bohr uit. Bohr’s
quantumtheoretische beschrijving van het atoommodel bevatte nog steeds klassieke
elementen zoals impuls, energie en plaats. Hiermee zou zijn quantumtheorie in
strijd met zichzelf kunnen zijn. De schrijver wil daarom in het hoofdstuk de
volgende stelling bewijzen:
“Bohr was never a narrow empiricist (and never became a positivist either). His quantum theory, far from being contradictory, provided at any stage an analysis of its relation to classical theory that conciliated the persisting recourse to classical concepts with quantum discontinuity. Most important, Bohr realized that certain fundamental concepts could still be used in the quantum theory because they could be defined through an application of classical theory, within its accepted range of validity.” (p. 82)
Bohr formuleerde na enig aarzelen in 1917 zijn postulaten, omdat hij zich bewust was van de tekortkomingen van zijn theorie. Deze postulaten beschreef hij in puur quantummechanische concepten enerzijds of goed gedefinieerde klassieke concepten. Hiermee hoopte hij zijn theorie voldoende te hebben ondersteund. Dit bleek zo te zijn toen Heisenberg in 1925 zijn matrixmechanica baseerde op precies dezelfde postulaten die Bohr in 1918 verwoorden in zijn essay “On quantum theory of line spectra”: het postulaat over de stationaire toestanden en het postulaat over de relatie ?E = hv.
Bohr’s theorie stond open voor grote revisies en was dus opzettelijk incompleet om nieuwe ingrepen toe te staan, tot aan 1925 toen Bohr zijn idee over elektronbanen compleet los liet. Een belangrijke principe om deze structurele wijzigingen te ‘dirigeren’ werd het correspondentie principe, waarmee inductief of deductief conclusies getrokken konden worden. Volgens criticus Pauli verloor dit principe uiteindelijk zijn deductieve karakter.
The Bohr Atom
Postulates and Principles
Harmonic Interplay
A Crisis
The Virtual Orchestra
Matrix Mechanics
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Hoofdstuk 10 ‘It was the spring of hope, it was the winter of
despair’
page 189 – 190
1. Ehrenfest on adiabatics. Paul Ehrenfest studied physics in his native Vienna, where his contact with Boltzmann (under whose guidance he obtained the Ph.D.) was decisive in directing him to his principal scientific devotion, statistical physics. As was noted earlier (5d, e) that was the branch of physics which had served Planck and Einstein as their prime tool in their earliest work on quantum theory. Ehrenfest studied their papers carefully. As a result he became probably the first after the founders to publish on quantum problems, beginning in 1905. These early papers already showed what Einstein later called 'his unusually well developed faculty to grasp the essence of a theoretical notion, to strip a theory of its mathematical accoutrements until the simple basic idea emerged with clarity. This capacity made him... the best teacher in our profession whom I have ever known.' He was respected by all who knew his work except by himself.
Ehrenfest's initial reactions to Bohr's work were decidedly negative. In 1913 he wrote to Lorentz: 'Bohr's work on the quantum theory of the Balmer formula . .. has driven me to despair. If this is the way to reach the goal I must give up doing physics.' After Sommerfeld had come out with his work on fine structure, Ehrenfest wrote to him: 'Even though I consider it horrible that this success will help the preliminary but still completely monstrous Bohr model on to new triumphs, I nevertheless wish physics at Munich further success along this path.'
Ehrenfest's contribution of interest to us here, his 'adiabatic principle', was inspired by his critical analysis of the contributions by Planck and Einstein, not by those of Bohr, even though, as it turned out, the main applications of his principle were to issues in atomic physics. He published this work in ever more systematic detail in the course of the years 1911-16, most of it from Leiden where, since late 1912, he had been installed as successor to Lorentz.
The gist of the adiabatic principle can be stated as follows. If you give me the quantum rules for a particular system, then I can tell you the rules for a whole class of other systems. The proof is based on the hypothesis that Newtonian mechanics continues to apply as long as systems are in a stationary state, while the quantum theory only comes in to account for jumps from one such state to another. As Bohr had stressed from the beginning, this assumption also applied to his own work. Here I shall only indicate Ehrenfest's reasoning in terms of a special case: the general argument is too technical for the style adopted in this book.
Consider a system in periodic motion characterized by a single quantum number, call it n, and by specific values of parameters such as the nuclear charge, the intensity of some external field of force, etc. Now let these parameters be subjected to extremely slow and smooth changes, called adiabatic transformations (a term borrowed from thermodynamics). What happens to the number n? The adiabatic principle says: n does not change, it remains invariant. In his unpublished paper of 1916, Bohr put it like this: 'The great importance in the Quantum theory of this invariant character has been pointed out by P. Ehrenfest; it allows us by varying the external conditions to obtain a continuous transformation through possible states from a stationary state of any periodic system to the state corresponding with the same value of n of any other such system containing the same number of moving particles.' The 'other' system may be quite different from the starting system. For example, one can connect in this way the rule for quantizing a (one-dimensional) oscillator with the one for the (non-relativistic) Bohr atom. This clearly brings much improved coherence to the old quantum theory: one still did not know why any system is quantized but now one could at least link the quantization of vastly distinct systems.
Ehrenfest knew that already in 1914 Einstein had recognized the importance of his work but was not aware of Bohr's unpublished paper of 1916. When in 1918 Bohr incorporated this manuscript in a major paper he stressed 'the great progress ... recently obtained by Ehrenfest'. When in that year Kramers returned to Copenhagen from a visit to Leiden, with regards from Ehrenfest, Bohr sent him a letter, the beginning of a long correspondence, in which he wrote: 'I hope very much to meet you when the war is over.' In 1922 Ehrenfest wrote to Bohr about the adiabatic principle: 'I have never discovered anything - and quite surely never will discover anything - that I can love so fervently.'
The two men first met in 1919 when Bohr gave a lecture in Leiden on 'Problems of the atom and the molecule'82 and attended Kramers' thesis defense. In December 1921 Ehrenfest lectured in Copenhagen. He had come to venerate and love Bohr. In 1919, right after Bohr's visit to Leiden, he wrote to him: 'You had gone, the music had faded away.' When in 1929 he took along his gifted young student Hendrik Casimir to a physics meeting in Copenhagen he said to him along the way: 'Now you are going to meet Niels Bohr and that is the most important thing to happen in the life of a young physicist.'
On Adiabatic Changes of a System in Connection with the Quantum Theory [Ann. Physik 51, 327 - 352, 1916]
Le Principe de Correspondance [Solvay Conference, 1921]
Adiabatische Transformationen in der Quantentheorie und ihre Behandlung durch Niels Bohr [Naturw. 11, 543 - 550, 1923]
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