Article ID: CBB000933683

The Classical Roots of Wave Mechanics: Schrödinger's Transformations of the Optical-Mechanical Analogy (2009)


In the 1830s, W. R. Hamilton established a formal analogy between optics and mechanics by constructing a mathematical equivalence between the extremum principles of ray optics (Fermat's principle) and corpuscular mechanics (Maupertuis's principle). Almost a century later, this optical-mechanical analogy played a central role in the development of wave mechanics. Schrödinger was well acquainted with Hamilton's analogy through earlier studies. From Schrödinger's research notebooks, we show how he used the analogy as a heuristic tool to develop de Broglie's ideas about matter waves and how the role of the analogy in his thinking changed from a heuristic tool into a formal constraint on possible wave equations. We argue that Schrödinger only understood the full impact of the optical-mechanical analogy during the preparation of his second communication on wave mechanics: Classical mechanics is an approximation to the new undulatory mechanics, just as ray optics is an approximation to wave optics. This completion of the analogy convinced Schrödinger to stick to a realist interpretation of the wave function, in opposition to the emerging mainstream. The transformations in Schrödinger's use of the optical-mechanical analogy can be traced in his research notebooks, which offer a much more complete picture of the development of wave mechanics than has been previously thought possible.

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Article Dongen, Jeroen van; Dieks, Dennis; Uffink, Jos; Kox, A. J. (2009) On the History of the Quantum: Introduction to the HQ2 Special Issue. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics (p. 277). unapi

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Authors & Contributors
Perovic, Slobodan
Boido, Guillermo
Rodríguez, Victor
Hankins, Thomas L.
Hanle, Paul A.
Lochak, Georges
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Physics in Perspective
Isis: International Review Devoted to the History of Science and Its Cultural Influences
Foundations of Physics
Revue des Questions Scientifiques
科学史研究 Kagakusi Kenkyu (History of Science)
Associação de Filosofia e História da Ciência do Cone Sul
Yale University Press
Drew University
MIT Press
Quantum mechanics
Philosophy of science
Theoretical physics
Schrödinger, Erwin
Broglie, Louis Victor Pierre Raymond de
Bohr, Niels Henrik David
Heisenberg, Werner
Dirac, Paul Adrien Maurice
Einstein, Albert
Time Periods
20th century, early
20th century
19th century
Paris (France)
Dublin (Ireland)
Trinity College Dublin

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