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Letters on wave mechanics: Albert Einstein, Erwin Schroedinger, Max Planck [and] H. A. Lorentz

Albert Einstein, Erwin Schrödinger, Max Planck +2 more

Jan 1, 19680 citations

Briefe zur Wellenmechanik : Schrödinger - Planck - Einstein - Lorentz

Albert Einstein, H. A. Lorentz, Max Planck +2 more

Jan 1, 19631 citation

Erwin Schrödinger — Wave Mechanics

IMPERIAL COLLEGE PRESS eBooksNov 1, 20110 citations

Schrödinger–Planck–Einstein–Lorentz Briefe Zur Wellenmechanik

Lewis Elton

Edited by K. Przibram Vienna: Springer-Verlag. 1963. Pp. 67. Price 18s. The majority of these letters belong to those exciting months of April to June 1926, during which Schrödinger struggled with others as well as with himself in order to smooth out the difficulties of his theory. They make fascinating reading.

Physics BulletinJul 1, 19644 citations

Euler-Korteweg vortices: A fluid-mechanical analogue to the Schrödinger and Klein-Gordon equations

D. M. F. Bischoff van Heemskerck

Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schrödinger and Klein-Gordon equations. By assuming that the angular momentum of an irrotational vortex in an inviscid, barotropic, isothermal fluid with sound speed c is equal in magnitude to the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity equations of an Euler-Korteweg vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is formally equivalent to Schrödinger's equation. The model is shown to yield analogues to de Broglie wavelength, the Einstein-Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wave field of a vortex in convection requires the Lorentz transformation and yields a wave equation mathematically equivalent to the Klein-Gordon equation, with Schrödinger's equation appearing as the low-Mach-number limit.Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schrödinger and Klein-Gordon equations. By assuming that the angular momentum of an irrotational vortex in an inviscid, barotropic, isothermal fluid with sound speed c is equal in magnitude to the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity equations of an Euler-Korteweg vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is formally equivalent to Schrödinger's equation. The model is shown to yield analogues to de Broglie wavelength, the Einstein-Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wave field of a vortex in convection requires the Lorentz transformation and yields a wave equation mathematically equivalent to the Klein-Gordon equation, with Schrödinger's equation appearing as the low-Mach-number limit.

quant-pharXiv:2512.23771AIP AdvancesDec 30, 20250 citations

Some Comments on the Foundations of Physics

Per‐Olov Löwdin

This pedagogical monograph describes some of the fundamental laws of physics. The derivations are, however, obtained from a rather unconventional point of view. The Lorentz transformations and the special theory of relativity are derived without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism are derived without the help of Planck's constant. By the use of Schrödinger's idea of "quantization as an eigenvalue problem", the foundations of wave mechanics are discussed as a mathematical problem without reference to Planck's constant. Finally, theThis pedagogical monograph describes some of the fundamental laws of physics. The derivations are, however, obtained from a rather unconventional point of view. The Lorentz transformations and the special theory of relativity are derived without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism are derived without the help of Planck's constant. By the use of Schrödinger's idea of "quantization as an eigenvalue problem", the foundations of wave mechanics are discussed as a mathematical problem without reference to Planck's constant. Finally, the

WORLD SCIENTIFIC eBooksOct 1, 19985 citations

Letters on wave mechanics : Schrödinger, Planck, Einstein, Lorentz

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Letters on wave mechanics : Schrödinger, Planck, Einstein, Lorentz

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