Louis de Broglie's revolutionary conjecture in 1923 that massive particles have a wave character played a central role in the invention of quantum mechanics by Heisenberg and Schrödinger. The experimental verification of the wave nature of atoms followed soon thereafter, when Otto Stern demonstrated the reflection and diffraction of atoms at metal surfaces. While these experiments can be considered as marking the birth of atom optics, a major stumbling block toward its further development is the fact that at room temperature, the thermal de Broglie wavelength is only of the order of a few hundredths of nanometers.
Louis de Broglie's revolutionary conjecture in 1923 that massive particles have a wave character played a central role in the invention of quantum mechanics by Heisenberg and Schrödinger. The experimental verification of the wave nature of atoms followed soon thereafter, when Otto Stern demonstrated the reflection and diffraction of atoms at metal surfaces. While these experiments can be considered as marking the birth of atom optics, a major stumbling block toward its further development is the fact that at room temperature, the thermal de Broglie wavelength is only of the order of a few hundredths of nanometers.
Abstract The contributions of Otto Stern to the discovery of wave-particle duality of matter particles predicted by de Broglie are reviewed. After a short introduction to the early matter-vs-wave ideas about light, the events are highlighted which lead to de Broglie’s idea that all particles, also massive particles, should exhibit wave behavior with a wavelength inversely proportional to their mass. The first confirming experimental evidence came for electrons from the diffraction experiments of Davisson and Germer and those of Thomson. The first demonstration for atoms, with three orders of magnitude smaller wave lengths, came from Otto Stern’s laboratory shortly afterwards in 1929 in a remarkabletour de forceexperiment. After Stern’s forced departure from Hamburg in 1933 it took more than 40 years to reach a similar level of experimental perfection as achieved then in Stern’s laboratory. Today He atom diffraction is a powerful tool for studying the atomic and electronic structure and dynamics of surfaces. With the advent of nanotechnology nanoscopic transmission gratings have led to many new applications of matter waves in chemistry and physics, which are illustrated with a few examples and described in more detail in the following chapters.
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.
Since the beginning of the 20th century, physicists have known that light must be considered as both a wave and a particle. Some properties of light – such as diffraction – can only be explained by treating it as waves, while others – like the photoelectric effect – can only be explained by treating it as particles. In the 1920s Louis de Broglie suggested that this wave–particle duality, which lies at the heart of the counterintuitive laws of quantum mechanics, could be extended to massive particles. In other words, electrons, atoms and molecules should diffract and interfere just like light does.
Louis-Victor de Broglie secured his place in the history of quantum physics by proposing the existence of matter waves. Following the concept accepted early in the twentieth century that light waves could display properties characteristic of particles (photons), de Broglie suggested the complementary principle that particles could display properties characteristic of waves. Within a few years, this far-reaching proposal was experimentally verified. The well-known formula for the wavelength λ of the wave associated with a particle of momentum p, namely λ=h/p, does not appear in de Broglie’s original paper, which was published in this journal in 1924. What is derived from the starting assumption that the frequency of the wave is the rest energy of the particle divided by Planck’s constant h, is the wave's velocity, which turns out to be c2/v, where v is the particle’s velocity. This velocity, being superluminal, means that the wave cannot transport energy. De Broglie called it a phase wave and postulated a group of such waves having virtually, but not exactly, the same velocity and wavelength. The group velocity of such a large number of almost identical phase waves is then shown, very satisfactorily, to be equal to the velocity of the particle. The proposal by de Broglie inspired Schrödinger to develop the mathematical foundations of wave mechanics. Whereas in conventional quantum theory, phase waves are considered fictional, de Broglie considered them to have a certain physical reality, renaming them pilot or guiding waves – a concept developed later by Bohm in 1952.
Bohr's response in 1925 to the failure of the Bohr–Kramers–Slater theory was, as we have seen, to regard wave–particle duality as having a formal, rather than realistic, significance; he saw it as a ‘limitation of our usual means of visualization’. That same year, however, wave–particle duality was generalised by Louis-Victor de Broglie to cover the theory of matter. Moreover, the advent of quantum mechanics (i.e. matrix mechanics and wave mechanics), rather than dispelling the duality problem, heightened it. How did Bohr respond to these new developments in the quantum theory? A matter of waves In the autumn of 1923 de Broglie put forward the extremely bold hypothesis that any particle whatever is associated with a wave whose wavelength λ and frequency ν are proportional to the particle's momentum and energy respectively: λ = h / p , v = E / h . De Broglie regarded his hypothesis as the basis of a new mechanics, a wave mechanics related to classical mechanics in the same way as wave optics is related to ray optics. On this view the trajectory of a particle corresponds to the ray of the wave associated with it (i.e. the normal to the equiphase surface of the wave), and the velocity of the particle corresponds to the group velocity of the wave. De Broglie suggested, moreover, that in certain circumstances particles should exhibit diffraction effects: a stream of electrons, for example, which passes through a slit in a screen should undergo diffraction.
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.