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arXiv:physics/0506211

A Wave Interpretation of the Compton Effect As a Further Demonstration of the Postulates of de Broglie

Ching-Chuan Su

Published Jun 29, 2005• 1 citation
arXivHTMLPDF

Abstract

The Compton effect is commonly cited as a demonstration of the particle feature of light, while the wave nature of matter has been proposed by de Broglie and demonstrated by Davisson and Germer with the Bragg diffraction of electron beams. In this investigation, we present an entirely different interpretation of the Compton effect based on the postulates of de Broglie and on an interaction between electromagnetic and matter waves. The speeds of interacting electrons in the Compton scattering are quite fast and its mechanism relies heavily on the mass variation. Thus, based on this wave interpretation, the Compton effect can be viewed as a further demonstration of the postulates of de Broglie for high-speed particles. In addition to the scattered wave, a direct radiation depending on the mass variation is predicted, which provides a means to test the wave interpretation.

DOI
10.48550/arxiv.physics/0506211

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The Compton effect is commonly cited as a demonstration of the particle feature of light, while the wave nature of matter has been proposed by de Broglie and demonstrated by Davisson and Germer with the Bragg diffraction of electron beams. In this investigation, we present an entirely different interpretation of the Compton effect based on the postulates of de Broglie and on an interaction between electromagnetic and matter waves. The speeds of interacting electrons in the Compton scattering are quite fast and its mechanism relies heavily on the mass variation. Thus, based on this wave interpretation, the Compton effect can be viewed as a further demonstration of the postulates of de Broglie for high-speed particles. In addition to the scattered wave, a direct radiation depending on the mass variation is predicted, which provides a means to test the wave interpretation.
Abstract We have seen that it took about two decades to fully realize that light or, generally, electromagnetic radiation has both wave and particle properties. The final proof came with the discovery of the Compton effect (Episode 31). Even Compton himself needed years before he saw that the particle picture of radiation was unavoidable in view of the experimental evidence. Still in the year of Compton’s publications, Louis de Broglie [1] on purely theoretical grounds proposed that the particle–wave duality not only holds for radiation but also for material particles, i.e., for particles with a rest mass such as the electron.
The fact that light has some of the properties of ordinary particles led Louis de Broglie, in 1924, to construct a theory on the proposition that photons are particles. In the theory of wave motions, there is in general a difference between the speed of waves of some uniquely defined frequency, and the speed of a localized pulse such as de Broglie proposed to associate with a moving particle. Most often, one wishes to know the de Broglie wavelength for particles of a given kinetic energy. C. J. Davisson and L. H. Germer deliberately used single crystals as targets, and proceeded to discover just the kind of behavior that de Broglie's hypothesis of particle waves predicted. The development of electron microscopy, with its use of extremely well collimated, highly monoenergetic electron beams, has led to some beautiful demonstrations of the wave properties of electrons in analogs of optical diffraction phenomena. The strong reflection is a wave-like phenomenon totally unexpected from the classical picture of electrons.
In 1924, de Broglie postulated that particles can behave like waves, thus complementing the observation by Einstein in 1905 that light can behave like particles. This wave–particle duality aspect for both particles and waves had a deep impact on the subsequent development of quantum mechanics. Some highly counterintuitive results, like the Heisenberg uncertainty relation and the Bose–Einstein condensation, that were motivated by wave–particle duality are discussed in this chapter. Following de Broglie’s hypothesis, a wave packet description for a particle is described. An analysis of the Heisenberg microscope is presented, thus motivating the Heisenberg uncertainty relation. The Davisson–Germer experiment that showed that electrons can behave like waves and the Compton effect that provided early conclusive evidence that light can behave like particles are also discussed.
The undergraduate courses on modern physics generally consider the particle interpretation of Compton effect. Motivated by a student's solution in an undergraduate examination on modern physics here we consider the wave characteristics of recoiled electrons in the Compton effect. The de Broglie wavelength, wave and clock frequency of the scattered electrons are expressed in terms of the wavelength and the frequency of the incident and the scattered photons respectively using the familiar particle interpretation of the Compton effect, where initially the electron is at rest and its spin is ignored. Both non-relativistic and relativistic cases are considered. Numerical values of de Broglie wavelength, wave and clock frequency of the scattered electron are calculated for an incident photon energy that was used in the original experiment of Compton as a function of the scattering angle of the recoiled electron. Considering the relativistic effects which are however insignificant for the de Broglie wavelength of the recoiled electron under these conditions, the minimum value obtained is in the range of X-rays. The non-relativistic de Broglie wave frequency obtained by neglecting the rest mass of the electron leads to an underestimation of its value. The implications of de Broglie wavelength and clock frequency for Compton scattering experiments are briefly discussed and possible extensions of the obtained mathematical formulations are indicated. The results are useful for understanding the wave-particle duality of the recoiled electron in the context of the Compton effect.
Compton scattering is usually explained in terms of the relativistic mass and momentum. Here, a mathematically equivalent and simple non-relativistic interpretation shows that the Compton frequency shift is equal to the de Broglie frequency associated with the moving charged particle (e.g., an electron). In this work, the moving electron is considered as a particle and the electromagnetic energy associated with it is shown to be proportional to the de Broglie frequency. This energy is released when its motion is arrested, as for example on a diffraction screen, where it causes the observed interfernce patterns. Thus, electrons transport electromagnetic energy from a source to a sink.