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Springer eBooks

Otto Stern and Wave-Particle Duality

Jan Peter Toennies

Published Jan 1, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1007/978-3-030-63963-1_23

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Grating Diffraction of Molecular Beams: Present Day Implementations of Otto Stern’s Concept

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Abstract When Otto Stern embarked on molecular-beam experiments in his new lab at Hamburg University a century ago, one of his interests was to demonstrate the wave-nature of atoms and molecules that had been predicted shortly before by Louis de Broglie. As the effects of diffraction and interference provide conclusive evidence for wave-type behavior, Otto Stern and his coworkers conceived two matter-wave diffraction experiments employing their innovative molecular-beam method. The first concept assumed the molecular ray to coherently scatter off a plane ruled grating at grazing incidence conditions, while the second one was based on the coherent scattering from a cleaved crystal surface. The latter concept allowed Stern and his associates to demonstrate the wave behavior of atoms and molecules and to validate de Broglie’s formula. The former experiment, however, fell short of providing evidence for diffraction of matter waves. It was not until 2007 that the grating diffraction experiment was retried with a modern molecular-beam apparatus. Fully resolved matter-wave diffraction patterns were observed, confirming the viability of Otto Stern’s experimental concept. The correct explanation of the experiment accounts for quantum reflection, another wave effect incompatible with the particle picture, which was not foreseen by Stern and his contemporaries.

Springer eBooks•Jan 1, 2021•1 citation

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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.

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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.

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Abstract Motivated by his interest in thermodynamics and the emerging quantum mechanics, Otto Stern (1888–1969) launched in 1919 his molecular beam method to examine the fundamental assumptions of theory that transpire in atomic, molecular, optical, and nuclear physics. Stern’s experimental endeavors at Frankfurt (1919–1922), Hamburg (1923–1933), and Pittsburgh (1933–1945) provided insights into the quantum world that were independent of spectroscopy and that concerned well-defined isolated systems, hitherto accessible only toGedankenexperiments. In this chapter we look at how Stern’s molecular beam research came about and review six of his seminal experiments along with their context and reception by the physics community: the Stern-Gerlach experiment; the three-stage Stern-Gerlach experiment; experimental evidence for de Broglie’s matter waves; measurements of the magnetic dipole moment of the proton and the deuteron; experimental demonstration of momentum transfer upon absorption or emission of a photon; the experimental verification of the Maxwell-Boltzmann velocity distribution via deflection of a molecular beam by gravity. Regarded as paragons of thoroughness and ingenuity, these experiments entail accurate transversal momentum measurements with resolution better than 0.1 atomic units. Some of these experiments would be taken up by others where Stern left off only decades later (matter-wave scattering or photon momentum transfer). We conclude by highlighting aspects of Stern’s legacy as reflected by the honors that have been bestowed upon him to date.

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De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.

Physics Essays•Sep 3, 2022•0 citations
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.
Abstract When Otto Stern embarked on molecular-beam experiments in his new lab at Hamburg University a century ago, one of his interests was to demonstrate the wave-nature of atoms and molecules that had been predicted shortly before by Louis de Broglie. As the effects of diffraction and interference provide conclusive evidence for wave-type behavior, Otto Stern and his coworkers conceived two matter-wave diffraction experiments employing their innovative molecular-beam method. The first concept assumed the molecular ray to coherently scatter off a plane ruled grating at grazing incidence conditions, while the second one was based on the coherent scattering from a cleaved crystal surface. The latter concept allowed Stern and his associates to demonstrate the wave behavior of atoms and molecules and to validate de Broglie’s formula. The former experiment, however, fell short of providing evidence for diffraction of matter waves. It was not until 2007 that the grating diffraction experiment was retried with a modern molecular-beam apparatus. Fully resolved matter-wave diffraction patterns were observed, confirming the viability of Otto Stern’s experimental concept. The correct explanation of the experiment accounts for quantum reflection, another wave effect incompatible with the particle picture, which was not foreseen by Stern and his contemporaries.
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.
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 Motivated by his interest in thermodynamics and the emerging quantum mechanics, Otto Stern (1888–1969) launched in 1919 his molecular beam method to examine the fundamental assumptions of theory that transpire in atomic, molecular, optical, and nuclear physics. Stern’s experimental endeavors at Frankfurt (1919–1922), Hamburg (1923–1933), and Pittsburgh (1933–1945) provided insights into the quantum world that were independent of spectroscopy and that concerned well-defined isolated systems, hitherto accessible only toGedankenexperiments. In this chapter we look at how Stern’s molecular beam research came about and review six of his seminal experiments along with their context and reception by the physics community: the Stern-Gerlach experiment; the three-stage Stern-Gerlach experiment; experimental evidence for de Broglie’s matter waves; measurements of the magnetic dipole moment of the proton and the deuteron; experimental demonstration of momentum transfer upon absorption or emission of a photon; the experimental verification of the Maxwell-Boltzmann velocity distribution via deflection of a molecular beam by gravity. Regarded as paragons of thoroughness and ingenuity, these experiments entail accurate transversal momentum measurements with resolution better than 0.1 atomic units. Some of these experiments would be taken up by others where Stern left off only decades later (matter-wave scattering or photon momentum transfer). We conclude by highlighting aspects of Stern’s legacy as reflected by the honors that have been bestowed upon him to date.
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.
De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.