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Schrödinger and the genesis of wave mechanics

Jürgen Renn

In the context of a new analysis of the notebooks of Erwin Schrödinger, the paper deals with the question of the relation between Schrödinger's creation of wave mechanics and the contemporary efforts by Werner Heisenberg and his colleagues to establish a new quantum mechanics. How can one explain, from a broader historical and epistemological perspective, the astonishing simultaneity and complementarity of these discoveries? The paper argues that neither the physical problems with which both approaches deal nor what ultimately turned out to be their common mathematical ground are sufficient to explain their complementarity. Instead, their closeness is explained by analyzing their common roots in classical mechanics and its transformation in the light of the most fundamental new quantum law, the relation between energy and frequency found by Planck. It is shown, in particular, that for both approaches a bridge between quantum and classical aspects involving this relation was crucial. In the case of Heisenberg, this bridge was given by Bohr’s correspondence principle. In the case of Schrödinger it was constituted by Hamilton’s optical-mechanical analogy.In the context of a new analysis of the notebooks of Erwin Schrödinger, the paper deals with the question of the relation between Schrödinger's creation of wave mechanics and the contemporary efforts by Werner Heisenberg and his colleagues to establish a new quantum mechanics. How can one explain, from a broader historical and epistemological perspective, the astonishing simultaneity and complementarity of these discoveries? The paper argues that neither the physical problems with which both approaches deal nor what ultimately turned out to be their common mathematical ground are sufficient to explain their complementarity. Instead, their closeness is explained by analyzing their common roots in classical mechanics and its transformation in the light of the most fundamental new quantum law, the relation between energy and frequency found by Planck. It is shown, in particular, that for both approaches a bridge between quantum and classical aspects involving this relation was crucial. In the case of Heisenberg, this bridge was given by Bohr’s correspondence principle. In the case of Schrödinger it was constituted by Hamilton’s optical-mechanical analogy.

ESI lectures in mathematics and physicsApr 11, 201316 citations

Principles of Schrödinger's Wave Mechanics

Reinhold Fürth

Elsevier eBooksJan 1, 19700 citations

Beam propagation in a thick lens using the quantum mechanics formulism

G Héctor Lorduy, L. Castellanos, Ángel Salazar +2 more

This paper has to do with the introduction of an algebraic operator method suitable for applications in a wide area of optics. The algebraic structure of this method allows us to derive results usually obtained by using the method of rays in classical optics. Here, we treat the propagation of electromagnetic waves in the framework of paraxial approach, where the paraxial wave equation is viewed as the Schrödinger's wave equation of quantum theory. The time variable of the Schrödinger's equation plays the role of a coordinate along the propagation axis. From this point of view, a formal analogy among the wave optics and quantum mechanics is constructed. In this work, the impulse response function (IRF) for a thick lens is obtained, and from this, the well known corresponding matrix transformation in classical optics is deduced.This paper has to do with the introduction of an algebraic operator method suitable for applications in a wide area of optics. The algebraic structure of this method allows us to derive results usually obtained by using the method of rays in classical optics. Here, we treat the propagation of electromagnetic waves in the framework of paraxial approach, where the paraxial wave equation is viewed as the Schrödinger's wave equation of quantum theory. The time variable of the Schrödinger's equation plays the role of a coordinate along the propagation axis. From this point of view, a formal analogy among the wave optics and quantum mechanics is constructed. In this work, the impulse response function (IRF) for a thick lens is obtained, and from this, the well known corresponding matrix transformation in classical optics is deduced.

AIP conference proceedingsJan 1, 20080 citations

Remarks on Schrödinger's wave mechanics

Viktor Trkal

Časopis pro pěstování matematiky a fysikyJan 1, 19280 citations

Wave Mechanics and the Schrödinger Equation

Maurice A. de Gosson

Fundamental theories of physicsJan 1, 20160 citations

Erwin Schrödinger’s Path to Wave Mechanics

Barry R. Masters

In 1926, Schrödinger invoked Hamilton’s optical-mechanical analogy that related ray optics and particle mechanics: His invention of wave mechanics related to particle mechanics as wave optics related to ray optics.

Optics and Photonics NewsFeb 1, 20146 citations

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

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