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Atlantis Press eBooks

Schrödinger’s Equation

Theo van Holten

Published Dec 9, 2016• 0 citations
Publisher

Abstract

A heuristic derivation of Schroedinger's equation is given, which makes it plausible that the beat patterns of the droplet theory satisfy this equation. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
DOI
10.2991/978-94-6239-234-2_11

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Introduction and Outline

Theo van Holten

Following a short history of quantum mechanics, an outline of the contents of this book is given. A model of an electron is derived by time-averaging the motion of a “zittering” electromagnetic singularity, and by adding an apparent force in the form of surface tension in order to remove false electrostatic effects due to the model simplification. This model of a deformable droplet of charge is adopted as a working hypothesis, to see what are the consequences of such a model. The consequences are mathematically worked out and are shown to lead to a quantitatively correct replica of quantum behaviour. Matter waves are shown to correspond to trains of beats in the pulsation of the droplet, and the correct value of Planck's constant is derived. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Atlantis Press eBooks•Dec 9, 2016•0 citations
In this lecture we give more details of an alternative approach to quantum scattering theory, initiated by V. Enss, This approach is based on a geometric analysis of the behavior for t→±∞t \rightarrow \pm \infty t→±∞ of the solutions of Schroedinger’s equation for initial data in the subspace of absolute continuity for the hamiltonian H . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Students in a quantum mechanics course are often introduced to the Schrödinger equation as the standard mathematical tool. However, rarely do students develop an understanding as to why the equation is the choice for modeling quantum phenomena or where it came from. While many books do have a heuristic derivation, they sometimes differ in their approach and often fail to give a satisfying explanation to the so-called canonical substitution of momentum. In this paper, we use de Broglie's hypothesis along with experimental results and theories to provide a heuristic derivation of the Schrödinger equation and of the the momentum operator.
Following a short history of quantum mechanics, an outline of the contents of this book is given. A model of an electron is derived by time-averaging the motion of a “zittering” electromagnetic singularity, and by adding an apparent force in the form of surface tension in order to remove false electrostatic effects due to the model simplification. This model of a deformable droplet of charge is adopted as a working hypothesis, to see what are the consequences of such a model. The consequences are mathematically worked out and are shown to lead to a quantitatively correct replica of quantum behaviour. Matter waves are shown to correspond to trains of beats in the pulsation of the droplet, and the correct value of Planck's constant is derived. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.