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Optics and Quantum Mechanics

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A Trajectory Description of Quantum Processes. I. Fundamentals

Part of the book series: Lecture Notes in Physics ((LNP,volume 850))

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Abstract

Although the concept of wave appears in the description of many different physical processes, it acquires a special relevance in the case of matter and radiation. The use of trajectories (or rays) and waves to describe both matter and radiation has led to a strongly intertwined historical development of both quantum mechanics and electromagnetism. In this sense, a brief overview of the wave formulation of electromagnetism (with particular emphasis on optics) is worth being presented here, for it will provide an alternative viewpoint to think quantum mechanics and, at the same time, the background necessary to understand later on the concept of photon trajectory. In this sense, this chapter will settle some general concepts which will be applied in the description of quantum phenomena by means of Bohmian mechanics.

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Notes

  1. 1.

    The terms wave optics, physical optics and undulatory optics are usually considered in the literature to denote the same: the part of optics described by the wave equation derived from Maxwell’s equations of electromagnetism. Throughout this monograph, the first term will be used preferably, since it allows a more direct conceptual connection with Schrödinger’s wave mechanics or quantum mechanics.

  2. 2.

    Of course, other solutions can also be devised. It is sufficient to assume a particular form (initial condition) for E and H satisfying the corresponding boundaries at a given time and then solving (4.2), which will give us the time-evolution of these fields.

  3. 3.

    In quantum mechanics, this is somehow similar to what happens within Feynman’s path-integral formulation [21] (see Sect. 3.4). In this case, the geometric optics ray is substituted by a classical (stationary) trajectory and the secondary wavelets are replaced by imaginary exponential functions, with their argument being the classical action evaluated along the corresponding varied (with respect to the classical trajectory) paths. As one approaches the classical limit, mainly contributions in a neighborhood of the classical trajectories are relevant.

  4. 4.

    In particular, the problem of finding a wave function for the photon is an issue which has received much attention in the literature [57–73]. It is remarkable that recently it has been shown experimentally [74] that such a wave function can be directly measured, which might open a very fruitful and interesting debate of unexpected implications.

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  1. Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

    Ángel S. Sanz & Salvador Miret-Artés

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Sanz, Á.S., Miret-Artés, S. (2012). Optics and Quantum Mechanics. In: A Trajectory Description of Quantum Processes. I. Fundamentals. Lecture Notes in Physics, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18092-7_4

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