The Methods of Construction in Schrödinger’s "Mitteilungen"
DOI:
https://doi.org/10.14394/filnau.2019.0009Słowa kluczowe:
Erwin Schrödinger, Mitteilungen, scientific laws, explanation, application, generalizationAbstrakt
The paper reconstructs the methods used by Schrödinger in the construction of wave mechanics as given in his four Mitteilungen. These methods are described from the point of view of modern philosophy of science, with a focus on the relationships between scientific theories and on the reconstruction of the structure of scientific laws and the relations between scientific laws. After reconstructing the derivation of the first equation in Mitteilung 1, it analyzes the methodology of the optical-mechanical analogy in Mitteilung 2 and reconstructs the two heuristic pathways that led to the construction of wave equations as the basis of wave mechanics in the first two Mitteilungen. Finally, it addresses the methods of generalization, application, and explanation by which the second, third, and fourth Mitteilungen are constructed.
Bibliografia
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Bruns H. (1895), “Das Eikonal,” Abhandlungen der königlich sächsischen Gesellschaft der Wissenschaften zu Leipzig 21, 323-436.
Conway A. W., Singe J. L. (1931), The Mathematical Papers of Sir William R. Hamilton, Vol. 1. Geometrical Optics, Cambridge: Cambridge University Press.
Darrigol O. (2009), “A Simplified Genesis of Quantum Mechanics,” Studies in the History and Philosophy of Modern Physics 40(2), 151-166. https://doi.org/10.1016/j.shpsb.2009.03.001
Darrigol O. (2012), A History of Optics, Oxford: Oxford University Press.
Darrigol O. (2014), Physics and Necessity, Oxford: Oxford University Press.
Hanzel I. (2007), “Leszek Nowak on Scientific Laws and Scientific Explanation” [in:] The Courage of Doing Philosophy, J. Brzeziński (ed.), Amsterdam: Rodopi, 167-178.
Hanzel I. (2008), “Idealizations and Concretizations in Laws and Explanations in Physics,” Journal for the General Philosophy of Science 39(2), 273-301. https://doi.org/10.1007/s10838-008-9073-x
Hanzel I. (2013), “Data, Phenomena and Mechanisms: The Logic of Construction of Bohr’s 1913 Theory of the Hydrogen Atom,” Organon F 20(3), 302-322.
Hanzel I. (2015), “Idealizations, Ceteris Paribus Clauses, Idealizational Laws, and All That,” Filozofia Nauki 23(1) [89], 5-26.
James J., Joas C. (2015), “Subsequent and Subsidiary?,” Historical Studies in the Natural Sciences 45(5), 641-702. https://doi.org/10.1525/hsns.2015.45.5.641
Joas C., Lehner C. (2009), “The Classical Roots of Wave Mechanics: Schrödinger's Transformations of the Optical-mechanical Analogy,” Studies in the History and Philosophy of Modern Physics 40(4), 338-351. https://doi.org/10.1016/j.shpsb.2009.06.007
Klein F. (1901), “Über das Brunsche Eikonal,” Zeitschrift für Mathematik und Physik 46, 372-375.
Mawhin J., Ronveaux A. (2010), “Schrödinger and Dirac Equations for the Hydrogen, and Laguerre Polynomials,” Archive for the History of Exact Sciences 64(4), 429-460. https://doi.org/10.1007/s00407-010-0060-3
Nowak L. (1971), U podstaw marksowskiej metodologii nauk, Warszawa: Państwowe Wydawnictwo Naukowe.
Nowak L. (1972), “Laws of Science, Theories, Measurement,” Philosophy of Science 39(4), 533-548. https://doi.org/10.1086/288479
Nowak L. (1977), Wstęp do idealizacyjnej teorii nauki, Warszawa: Państwowe Wydawnictwo Naukowe.
Nowak L., Nowakowa I. (2000), Idealization X, Amsterdam: Rodopi.
Post H. (1971), “Correspondence, Invariance, and Heuristics,” Studies in the History and Philosophy of Science 2(3), 213-255. https://doi.org/10.1016/0039-3681(71)90042-2
Radder M. (1991), “Heuristics and the Generalized Correspondence Principle,” British Journal for the Philosophy of Science 42(2), 195-226. https://doi.org/10.1093/bjps/42.2.195
Schrödinger E. (1926a), “Quantisierung als Eigenwertproblem (Erste Mitteilung),” Annalen der Physik 79, 361-376. https://doi.org/10.1002/andp.19263840404
Schrödinger E. (1926b), “Formeln für Summen von Binomialen. Eigenwertproblem des Atoms III. Zeeman- und Relativität als Störungen aufgefasst”, Notebook downloadable from the url-address https://phaidra.univie.ac.at/detail_object/o:164920
Schrödinger E. (1926c), “Quantisierung als Eigenwertproblem (Zweite Mitteilung),” Annalen der Physik 79, 489-527. https://doi.org/10.1002/andp.19263840602
Schrödinger E. (1926d), “Quantisierung als Eigenwertproblem (Dritte Mitteilung),” Annalen der Physik 80, 437-490. https://doi.org/10.1002/andp.19263851302
Schrödinger E. (1926e), “Quantisierung als Eigenwertproblem (Vierte Mitteilung),” Annalen der Physik 81, 109-139. https://doi.org/10.1002/andp.19263861802
Sommerfeld A., Runge I. (1911), “Anwendung der Vektorrechnung auf die Grundlagen der geometrischen Optik,” Annalen der Physik, 340(7), 277-298. https://doi.org/10.1002/andp.19113400705
Bruns H. (1895), “Das Eikonal,” Abhandlungen der königlich sächsischen Gesellschaft der Wissenschaften zu Leipzig 21, 323-436.
Conway A. W., Singe J. L. (1931), The Mathematical Papers of Sir William R. Hamilton, Vol. 1. Geometrical Optics, Cambridge: Cambridge University Press.
Darrigol O. (2009), “A Simplified Genesis of Quantum Mechanics,” Studies in the History and Philosophy of Modern Physics 40(2), 151-166. https://doi.org/10.1016/j.shpsb.2009.03.001
Darrigol O. (2012), A History of Optics, Oxford: Oxford University Press.
Darrigol O. (2014), Physics and Necessity, Oxford: Oxford University Press.
Hanzel I. (2007), “Leszek Nowak on Scientific Laws and Scientific Explanation” [in:] The Courage of Doing Philosophy, J. Brzeziński (ed.), Amsterdam: Rodopi, 167-178.
Hanzel I. (2008), “Idealizations and Concretizations in Laws and Explanations in Physics,” Journal for the General Philosophy of Science 39(2), 273-301. https://doi.org/10.1007/s10838-008-9073-x
Hanzel I. (2013), “Data, Phenomena and Mechanisms: The Logic of Construction of Bohr’s 1913 Theory of the Hydrogen Atom,” Organon F 20(3), 302-322.
Hanzel I. (2015), “Idealizations, Ceteris Paribus Clauses, Idealizational Laws, and All That,” Filozofia Nauki 23(1) [89], 5-26.
James J., Joas C. (2015), “Subsequent and Subsidiary?,” Historical Studies in the Natural Sciences 45(5), 641-702. https://doi.org/10.1525/hsns.2015.45.5.641
Joas C., Lehner C. (2009), “The Classical Roots of Wave Mechanics: Schrödinger's Transformations of the Optical-mechanical Analogy,” Studies in the History and Philosophy of Modern Physics 40(4), 338-351. https://doi.org/10.1016/j.shpsb.2009.06.007
Klein F. (1901), “Über das Brunsche Eikonal,” Zeitschrift für Mathematik und Physik 46, 372-375.
Mawhin J., Ronveaux A. (2010), “Schrödinger and Dirac Equations for the Hydrogen, and Laguerre Polynomials,” Archive for the History of Exact Sciences 64(4), 429-460. https://doi.org/10.1007/s00407-010-0060-3
Nowak L. (1971), U podstaw marksowskiej metodologii nauk, Warszawa: Państwowe Wydawnictwo Naukowe.
Nowak L. (1972), “Laws of Science, Theories, Measurement,” Philosophy of Science 39(4), 533-548. https://doi.org/10.1086/288479
Nowak L. (1977), Wstęp do idealizacyjnej teorii nauki, Warszawa: Państwowe Wydawnictwo Naukowe.
Nowak L., Nowakowa I. (2000), Idealization X, Amsterdam: Rodopi.
Post H. (1971), “Correspondence, Invariance, and Heuristics,” Studies in the History and Philosophy of Science 2(3), 213-255. https://doi.org/10.1016/0039-3681(71)90042-2
Radder M. (1991), “Heuristics and the Generalized Correspondence Principle,” British Journal for the Philosophy of Science 42(2), 195-226. https://doi.org/10.1093/bjps/42.2.195
Schrödinger E. (1926a), “Quantisierung als Eigenwertproblem (Erste Mitteilung),” Annalen der Physik 79, 361-376. https://doi.org/10.1002/andp.19263840404
Schrödinger E. (1926b), “Formeln für Summen von Binomialen. Eigenwertproblem des Atoms III. Zeeman- und Relativität als Störungen aufgefasst”, Notebook downloadable from the url-address https://phaidra.univie.ac.at/detail_object/o:164920
Schrödinger E. (1926c), “Quantisierung als Eigenwertproblem (Zweite Mitteilung),” Annalen der Physik 79, 489-527. https://doi.org/10.1002/andp.19263840602
Schrödinger E. (1926d), “Quantisierung als Eigenwertproblem (Dritte Mitteilung),” Annalen der Physik 80, 437-490. https://doi.org/10.1002/andp.19263851302
Schrödinger E. (1926e), “Quantisierung als Eigenwertproblem (Vierte Mitteilung),” Annalen der Physik 81, 109-139. https://doi.org/10.1002/andp.19263861802
Sommerfeld A., Runge I. (1911), “Anwendung der Vektorrechnung auf die Grundlagen der geometrischen Optik,” Annalen der Physik, 340(7), 277-298. https://doi.org/10.1002/andp.19113400705
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Opublikowane
2019-06-30
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Hanzel, I. (2019). The Methods of Construction in Schrödinger’s "Mitteilungen". Filozofia Nauki, 27(2), 17–37. https://doi.org/10.14394/filnau.2019.0009
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Filozofia Nauki | ISSN 1230-6894 | e-ISSN 2657-5868