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.
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.
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.
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 evolution of light theories began with Isaac Newton's corpuscular model, which explained reflection and refraction but could not account for diffraction and interference. In contrast, Christiaan Huygens proposed a wave theory, explaining light's behavior through an ether-based medium, supported by his principle that each point in a wavefront acts as a secondary source. This idea was experimentally supported in the early nineteenth century when Thomas Young's double-slit experiment revealed an interference pattern, affirming light's wave nature. Later, James Clerk Maxwell unified electricity and magnetism, establishing light as an electromagnetic wave and extending the electromagnetic spectrum beyond visible light. In the twentieth century, Einstein's photoelectric effect introduced the concept of wave-particle duality, demonstrating that light behaves as discrete photons. Soon after, Louis de Broglie extended the idea of wave-particle duality to matter, a prediction confirmed in 1927 when Clinton Davisson and Lester Germer observed electron diffraction from a crystal and, independently, G.P. Thomson demonstrated electron diffraction through thin films, both proving that electrons also exhibit wave-like properties. This concept was dramatically visualized by Claus Jonsson's 1961 electron double-slit experiment. Recently, the ALICE collaboration observed quantum interference patterns at the femtometer scale in ultra-relativistic nuclear collisions, pushing quantum interference studies to new frontiers.
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.
[M]odern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language. Werner Heisenberg Basic framework Prerequisites: Appendix C, §1B(ii). Near the beginning of the twentieth century, physicists realized that electromagnetic waves sometimes exhibited particle-like properties, as if light were composed of discrete ‘photons’. In 1923, Louis de Broglie proposed that, conversely, particles of matter might have wave-like properties. This was confirmed in 1927 by C. J. Davisson and L. H. Germer and, independently, by G. P. Thompson, who showed that an electron beam exhibited an unmistakable diffraction pattern when scattered off a metal plate, as if the beam were composed of ‘electron waves’. Systems with many interacting particles exhibit even more curious phenomena. Quantum mechanics is a theory which explains these phenomena. We will not attempt here to provide a physical justification for quantum mechanics. Historically, quantum theory developed through a combination of vaguely implausible physical analogies and wild guesses motivated by inexplicable empirical phenomena. By now, these analogies and guesses have been overwhelmingly vindicated by experimental evidence. The best justification for quantum mechanics is that it ‘works’, by which we mean that its theoretical predictions match all available empirical data with astonishing accuracy.