Einstein assumed duality between radiation and particles. Experiments involving electrons and diffraction effects are described to illustrate such behaviors. Classical physics and Einstein’s findings unmistakably demonstrated that light possessed both wave and particle properties. The responses of electrons in electric and magnetic fields are evidence for their existence as charged particles. The relationship between particle- and wave-like behavior was given by de Broglie in 1924. The dual nature of electrons was demonstrated experimentally by Davisson and Germer, when studying the diffraction of a stream of electrons. The reflection or diffraction of a beam of electromagnetic radiation can be expected to change its intensity, but changes in its wavelength would not ordinarily be anticipated. Photons and electrons may be described in terms of waves, but this approach has inherent limitations. The greater the attempt that is made to study the nature or behavior of a photon or a particle, the greater will be the uncertainty or error of the measurements.
Einstein assumed duality between radiation and particles. Experiments involving electrons and diffraction effects are described to illustrate such behaviors. Classical physics and Einstein’s findings unmistakably demonstrated that light possessed both wave and particle properties. The responses of electrons in electric and magnetic fields are evidence for their existence as charged particles. The relationship between particle- and wave-like behavior was given by de Broglie in 1924. The dual nature of electrons was demonstrated experimentally by Davisson and Germer, when studying the diffraction of a stream of electrons. The reflection or diffraction of a beam of electromagnetic radiation can be expected to change its intensity, but changes in its wavelength would not ordinarily be anticipated. Photons and electrons may be described in terms of waves, but this approach has inherent limitations. The greater the attempt that is made to study the nature or behavior of a photon or a particle, the greater will be the uncertainty or error of the measurements.
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
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.
Classical physics identified matter with particles and radiation with waves. Although these descriptions accounted for a large number of very important facts, it became apparent at the beginning of the twentieth century that other phenomena, such as blackbody radiation and photoelectric effect, are satisfactorily explained only if radiation is described in terms of particles. Louis de Broglie developed a theory according to which, conversely, matter has wave properties. As an outcome of this theory, he was able to write down a formula relating the corresponding wavelength with the momentum of the particle. Diffraction patterns characterize waves, and the basic fact that corroborated the validity of the notion of matter waves was that the Davisson and Germer experiment proved electrons can be diffracted. In classical optics the simplest experiment displaying this phenomenon is the well-known Young two-slit experiment, in which a beam of light is passed through a diaphragm with two slits.
This chapter discusses the conceptual foundations of quantum mechanics in the context of matter. Classical physics identified matter with particles and radiation with "waves." Although this description accounted for a large number of very important facts, it became apparent around the turn of the century that other phenomena, such as blackbody radiation and photoelectric effect, are satisfactorily explained only if radiation is described in terms of particles. Sometime later the hypothesis that, conversely, matter has wave properties was proposed by Louis de Broglie and was confirmed by the Davisson-Germer experiment of electron diffraction. In this experiment and similar ones, an electron beam was passed through a regular lattice (crystal), and subsequently showed the well-known diffraction patterns that are characteristic of waves. These results confirmed the theoretical predictions that a monoenergetic electron beam should be described by a plane wave and that the wave vector k of the wave should be related to the momentum p of an individual electron.