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Journal of the Physical Society of Japan

Relativistic Schrödinger Equations and the Particle-Wave Duality

U. Ochs, M. Sorg

Published Apr 15, 1995• 2 citations
Publisher

Abstract

The theory of the Relativistic Schrodinger Equations can be extended to many-particle systems and yields a local-realistic explanation of the well-known paradoxes of conventional quantum mechanics (i.e. Bohm-Aharonov effect and double-slit experiment). Within the new framework, it becomes obvious that the particle-wave duality does apply in the same way to both the elementary objects (e.g. electrons) and to arbitrarily complex material systems (e.g. nucleons, heavy atoms, molecules etc.).

DOI
10.1143/jpsj.64.1120

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The theory of the Relativistic Schrodinger Equations can be extended to many-particle systems and yields a local-realistic explanation of the well-known paradoxes of conventional quantum mechanics (i.e. Bohm-Aharonov effect and double-slit experiment). Within the new framework, it becomes obvious that the particle-wave duality does apply in the same way to both the elementary objects (e.g. electrons) and to arbitrarily complex material systems (e.g. nucleons, heavy atoms, molecules etc.).
The simplest but deepest questions of the philosophy of quantum mechanics are these: Are quantum systems waves, or are they particles? Are they both or are they neither? When light bounces an electron out of the surface of an alkali metal it behaves like a particle. Light carries momentum but also a punch. Just as there is no such thing as half a punch, so there is no such thing as half a quantum of light. On the other hand, the shadow formed on a screen by an object has soft edges, edges which get softer as the object is moved away from the screen. Light exhibits the phenomena of diffraction and interference and so is wavelike. This dual behaviour of light, and indeed of matter itself, is called wave-particle duality. The wave nature of a quantum system is reflected in wave mechanics which assigns a wave-function to the system. But the dual nature of light was noticed before Schrodinger developed the wave-mechanical formalism in 1926. In fact, it goes back at least as far as Einsteins explanation of the photoelectric effect in 1905. Wave-particle duality is not something that arises within the quantum mechanical formalism. It is something which is expressed within it, and is something which is best discussed in terms of the paradoxes that quantum experiments force upon physics. In fact, the simplest and most immediately disturbing of the quantummechanical paradoxes arise out of wave-particle duality. We take the two-slit experiment and the delayed-choice experiment as examples.
The wave-particle duality for light has been well established by various experiments, such as Young’s double slit experiment and the photoelectric effect. This led de Broglie to propose that a particle also has wave characteristics. Schrödinger further established the wave equation for a moving particle. Many times, quantum mechanics textbooks do not show how Schrödinger’s equation was developed in an intuitive manner that is appropriate at the undergraduate level. This article presents a new approach for introducing Schrödinger’s equation. This new approach starts with Maxwell’s equations and then applies the quantized energy of a light wave and special relativity. This more intuitive approach should help undergraduate students understand the origin of Schrödinger’s equation in a more natural way.
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Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Based on the unified theory of wave-particle duality, a straightforward derivation of the Schrodinger equations is presented where previously no such derivation was considered to be possible. A new theory of quantum diffraction is subsequently developed.
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Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.