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Oxford University Press eBooks

The Duality of Particles and Waves: The Split Personality of Electrons

Christopher C. Gerry, Kimberley M. Bruno

Published Feb 21, 2013• 0 citations
Publisher

Abstract

This chapter discusses the dual nature of small particles, focusing on electrons. It begins by describing how the classical laws of physics, which were mostly established by the start of the twentieth century, did not work very well when applied on the atomic scale. In order to explain the atomic-scale phenomena, a new kind of physics was invented in the 1920s. This new physics was called quantum physics, or quantum mechanics. It applied to the world on the scale of the atom—the microscopic world, or microworld. The discussions then turn to an experiment involving ‘quantum’ coins; the difference between superposition state and mixed state; light, waves, and interference; and interference with electrons.

DOI
10.1093/acprof:oso/9780199666560.003.0002

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This chapter discusses the dual nature of small particles, focusing on electrons. It begins by describing how the classical laws of physics, which were mostly established by the start of the twentieth century, did not work very well when applied on the atomic scale. In order to explain the atomic-scale phenomena, a new kind of physics was invented in the 1920s. This new physics was called quantum physics, or quantum mechanics. It applied to the world on the scale of the atom—the microscopic world, or microworld. The discussions then turn to an experiment involving ‘quantum’ coins; the difference between superposition state and mixed state; light, waves, and interference; and interference with electrons.
Quantum mechanics, as a fundamental theory describing the microscopic world, has driven a revolution in physics over the past century. The wave-particle duality of electrons, as one of the core features of quantum mechanics, challenges the traditional understanding of matter in classical physics. Through wave-particle duality, electrons exhibit wave-like behavior in certain experiments and particle-like properties in others. This paper explores key concepts of quantum mechanics, such as the wave function and the Schrödinger equation, and verifies the wave and particle nature of electrons through experiments such as the double-slit experiment and Compton scattering. In addition, this paper discusses the integration of quantum field theory and quantum mechanics, emphasizing the profound impact of electron duality on modern physics and quantum technology. With the continuous development of quantum technology, the duality of electrons not only provides a theoretical foundation for fields such as quantum computing and quantum communication but also offers new directions for technological innovation in the future.
At the atomic scale, the distinction between particles and waves breaks down. The realization, early in the twentieth century, that light consists of discrete packages, or “photons,” prompted the converse suggestion that particles could behave like waves. Confirmation of this idea came in 1927, from an experiment involving the scattering of electrons from a crystal. Today, “wave-particle duality” is central to quantum mechanics, and the wave properties of subatomic particles are widely used in microscopy and crystallography. Electron diffraction techniques are widely used to characterize atomic arrangements on solid surfaces and inside thin films, and to investigate the structures of molecules in gases. The dual nature of waves and particles is part of the “spookiness” of quantum mechanics, which cannot be explained in any classical way. It used to be that one could only imagine an experiment that would simultaneously demonstrate the particle and wave nature 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.
By the beginning of the twentieth century, classical physics had accumulated many contradictions that could only be resolved by changing the main concepts of space and time (Einstein’s theory of relativity, Chapter P1) and the laws of motion of particles on atomic scales (quantum mechanics). The first quantum concepts appeared at the very beginning of the century (Planck’s formula for thermal radiation and Einstein’s formula for photoeffect, Chapter P5), but quantum mechanics as a closed science was not constructed until the end of the 1920s.
One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.
This chapter introduces fundamental concepts of modern physics that emerged from groundbreaking experiments and theories in the early 20th century. It begins by exploring the photoelectric effect, which demonstrates the particle nature of light (photons) and provides a basis for mathematical analysis of this phenomenon. The chapter then discusses Bragg diffraction and the concept of the wave function, illustrating the wave nature of particles such as electrons, protons, and neutrons, and introducing the idea of wave-particle duality. The probability distribution for an electron, whether trapped in a well or traveling freely, is also examined. Rutherford scattering is presented as a pivotal experiment that revealed the existence of the positively charged atomic nucleus. The chapter further explores atomic spectra, explaining how the discrete wavelengths of emitted light indicate that atomic electrons have restricted, quantized energy levels. The Bohr model of the atom is described and mathematically analyzed to predict the spectrum of hydrogen. Finally, the chapter covers the Balmer-Rydberg formula for mathematically analyzing the spectrum of hydrogen. The content is organized into sections covering the photoelectric effect, Bragg diffraction and the wave function, Rutherford scattering, atomic spectra, and a summary of the key concepts. This chapter provides an introduction to the revolutionary ideas of modern physics, including the dual nature of light and matter and the quantized nature of the atom. The chapter includes numerous worked examples and concludes with problems for the student to apply their knowledge.