The classical roots of wave mechanics: Schrödinger's transformations of the optical-mechanical analogy

Joas, Christian; Lehner, Christoph

doi:10.1016/j.shpsb.2009.06.007

Cited by 59 publications

(26 citation statements)

References 23 publications

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“…Today, contrary to OQT, the classical physics enters implicitly in the opticalmechanic analogy (based on the Hamilton-Jacobi theory [Fetter 2003]) of Schrödinger in the deduction of his equation [Joas 2009, Köberle 1979, Wessels 1977 and explicitly just in some specific potentials inspired on classical expressions (e.g., the harmonic and Coulombian ones [Eisberg 1961]) needed to solve the equation.…”

Section: Discussionmentioning

confidence: 99%

Analysis of the Jun Ishiwara’s “The universal meaning of the quantum of action”

Pelogia

Brasil

2017

EPJ H

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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 "Proceedings 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 incorporated 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.

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Section: Discussionmentioning

confidence: 99%

Analysis of the Jun Ishiwara’s “The universal meaning of the quantum of action”

Pelogia

Brasil

2017

EPJ H

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“…[4][5][6] In fact, analogy between wave optics and quantum mechanics has been a highlighted subject, since the early developments of quantum mechanics. 7 This analogy is mathematically rooted in the similarity of dynamic process of par-axial optics domain and the dynamic quantum process as well as in an isomorphism between the time independent Schödinger equation and the Helmholtz equation. 8 Recently, analogy of quantum systems with classical optics is interesting, because of its enormous consequence both in fundamental quantum mechanics and in technological applications.…”

Section: Introductionmentioning

confidence: 99%

Realization of non-linear coherent states by photonic lattices

Dehdashti

Liu

et al. 2015

AIP Advances

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“…See, among other publications,Darrigol (1992) andJoas and Lehner (2009). Communicated by: Jed Buchwald.…”

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confidence: 97%

Explaining the laser’s light: classical versus quantum electrodynamics in the 1960s

Bromberg

2015

Arch. Hist. Exact Sci.

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The laser, first operated in 1960, produced light with coherence properties that demanded explanation. While some attempted a treatment within the framework of classical coherence theory, others insisted that only quantum electrodynamics could give adequate insight and generality. The result was a sharp and rather bitter controversy, conducted over the physics and mathematics that were being deployed, but also over the criteria for doing good science. Three physicists were at the center of this dispute, Emil Wolf, Max Born's collaborator on a canonical text on optics as a branch of classical electromagnetism, Roy J. Glauber, a student of Julian Schwinger and a high-energy particle theorist, and Leonard Mandel, both experimentalist and theorist and versed in the physics of photodetection. The story told here is thus one of three distinct research trajectories and of the explosion that occurred when, pushed into the well-financed field of laser studies, these trajectories collided.

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The classical roots of wave mechanics: Schrödinger's transformations of the optical-mechanical analogy

Cited by 59 publications

References 23 publications

Analysis of the Jun Ishiwara’s “The universal meaning of the quantum of action”

Analysis of the Jun Ishiwara’s “The universal meaning of the quantum of action”

Realization of non-linear coherent states by photonic lattices

Explaining the laser’s light: classical versus quantum electrodynamics in the 1960s

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