Wave–Particle Duality: De Broglie, Einstein, and Schrödinger

Dennis K. Ross

Carson L. Tang

J. Domínguez-Montes, E. L. Eisman

Caio Lima Firme

This chapter presents the double-slit experiment and Davisson-Germer’s corresponding experiment that proved the wave-like nature of the electron in 1927. Next, it shows the basics of the special theory of relativity which is used by de Broglie to obtain the wave-particle duality. Afterwards, it displays the most important properties of a periodic wave along with the concepts of travelling wave, composite wave, group velocity, wave packet and single wave packet. These sections are the basis for understanding the de Broglie’s work where he used the special theory of relativity, Einstein’s quantum theory of light and the features of the periodic waves to obtain his famous constant relation of the product of linear momentum (of a particle) and wavelength (of a wave) which became the most important quantum concept used by Schrödinger to develop the quantum wave theory. In the end, a do-it-yourself activity is also given in order to plot several wave packets. (153 words).

Constantinos Ragazas

The wave-particle duality of photons, as hypothesized by Einstein, was well accepted by the early 1920's. De Broglie's bold hypothesis in 1924, that all matter likewise has a wave-particle duality added further fuel to the fire in the development of Quantum Mechanics. It seared into the minds of physicists the wave-particle duality of Nature. Needless to say, this counter intuitive and bold assertion mystified the World beyond any sensible comprehension by common sense. The question often asked by ordinary people is what is the matter with de Broglie waves? We provide just this answer and demystify this 'matter' in this short paper.

Muhammad Suhail Zubairy

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.