Physics
Wave-Particle Duality
Wave-particle duality is a fundamental concept in quantum mechanics, stating that particles such as electrons and photons exhibit both wave-like and particle-like behavior. This means that they can display characteristics of both waves and particles depending on the experimental setup. The concept challenges classical physics' distinction between particles and waves, and is essential for understanding the behavior of subatomic particles.
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10 Key excerpts on "Wave-Particle Duality"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 4 Wave–Particle Duality Wave–particle duality postulates that all matter exhibits both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like particle and wave to fully describe the behavior of quantum-scale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer. This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which wave–particle duality is one aspect of the concept of complementarity, that a phenomenon can be viewed in one way or in another, but not both simultaneously. The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when competing theories of light were proposed by Christiaan Huygens and Isaac Newton: light was thought either to consist of waves (Huygens) or of corpuscles particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa). This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of non-relativistic quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; but because of their small wavelengths, the wave properties of macroscopic objects cannot be detected. Brief history of wave and particle viewpoints Aristotle was one of the first to publicly hypothesize about the nature of light, proposing that light is a disturbance in the element air.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 13 Wave–Particle Duality Wave–particle duality postulates that all matter exhibits both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like particle and wave to fully describe the behavior of quantum-scale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer. This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which wave–particle duality is one aspect of the concept of complementarity, that a phenomenon can be viewed in one way or in another, but not both simultaneously. The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when competing theories of light were proposed by Christiaan Huygens and Isaac Newton: light was thought either to consist of waves (Huygens) or of corpuscles particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa). This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of non-relativistic quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; but because of their small wavelengths, the wave properties of macroscopic objects cannot be detected. Brief history of wave and particle viewpoints Aristotle was one of the first to publicly hypothesize about the nature of light, proposing that light is a disturbance in the element air.
eBook - PDF- Mohammad Reza Pahlavani(Author)
- 2012(Publication Date)
- IntechOpen(Publisher)
2 The Physical Nature of Wave/Particle Duality Marcello Cini Università La Sapienza, Roma Italy 1. Introduction 1.1 Waves and particles in quantum mechanics In spite of the fact that the extraordinary progress of experimental techniques make us able to manipulate at will systems made of any small and well defined number of atoms, electrons and photons - making therefore possible the actual performance of the gedankenexperimente that Einstein and Bohr had imagined to support their opposite views on the physical properties of the wavelike/particlelike objects ( quantons ) of the quantum world - it does not seem that, after more than eighty years, a unanimous consensus has been reached in the physicist's community on how to understand their strange properties. Unfortunately, we cannot know whether Feynman would still insist in maintaining his famous sentence It is fair to say that nobody understands quantum mechanics. We can only discuss if, almost thirty years after his death, some progress towards this goal has been made. I believe that this is the case. I will show in fact that, by following the suggestions of Feynman himself, some clarification of the old puzzles can be achieved. This chapter therefore by no means is intended to provide an impartial review of the present status of the question but is focused on the exposure of the results of more than twenty years of research of my group in Rome, which in my opinion provide a possible way of connecting together at the same time the random nature of the events at the atomic level of reality and the completeness of their probabilistic representation by the principles of Quantum Mechanics.
eBook - PDF- Akira Tonomura(Author)
- 1998(Publication Date)
- World Scientific(Publisher)
Chapter 6 Wave-Particle Duality Up to here, when talking about electron interference phenomena, I have been taking it as a matter of course that electrons are waves. Since we have seen several kinds of interference patterns, you may have been convinced that electrons are waves like the water waves seen in Chapter 2. It also remains true, however, that electrons are particles. An electron is always a particle when detected and has never been divided into two or more pieces. You may think it is paradoxical that electrons have both wave nature and particle nature, but it is the most fundamental principle of quantum mechanics, the law of the microscopic world. Waves or Particles? The particle nature means that an electron is localized at a point, and the wave nature means that an electron is extended in a space. How can electrons have these apparently contradictory properties? The two-slit experiment demonstrating the essence of this problem is almost always introduced at the beginning of quantum mechanics textbooks. I would like to discuss this most important experiment in quantum mechanics here, though many of you may already know about it. The two-slit experiment is an interference experiment in which electrons or pho-tons are incident one by one onto two slits (Fig. 39). The time interval between them is so sparse that at most one electron or photon exists in the apparatus. The experiment using photons, in place of electrons, is described in S. Tomonaga's essay Trial of a Photon. In this essay, a prosecutor asserts that Miss Photon must have passed through one of the two slits since she has never been found split into two or more pieces. Note that a photon in Chinese characters can also be pronounced as Mitsuko, a girl's name. While she insists that the prosecutor is not right, her be-havior is inspected at the scene of the event. We send out photons one by one onto the two slits. The arrival of individual photons is recorded on the screen behind the two slits.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
CHAPTER 29 Particles and waves LEARNING OBJECTIVES After reading this module, you should be able to: 29.1 define wave–particle duality 29.2 explain the origin of Planck’s constant from blackbody radiation 29.3 use photon energy to explain in detail the photoelectric effect 29.4 use photon momentum to explain in detail the Compton effect 29.5 solve problems involving the de Broglie wavelength of a particle 29.6 calculate quantum uncertainty using the Heisenberg uncertainty principle. INTRODUCTION This photograph shows a highly magnified view of a female mosquito, made with a scanning electron microscope (SEM). In the twentieth century, physicists were astonished when it was discovered that particles could behave like waves. In fact, we will see in this chapter that there is a wavelength associated with a moving particle such as an electron. The microscope used for the photograph takes advantage of the electron wavelength, which can be made much smaller than that of visible light. It is this small electron wavelength that is responsible for the exceptional resolution of fine detail in the photograph. Source: Susumu Nishinaga / Science Source 29.1 The wave–particle duality LEARNING OBJECTIVE 29.1 Define wave–particle duality. The ability to exhibit interference effects is an essential characteristic of waves. For instance, section 27.2 discusses Young’s famous experiment in which light passes through two closely spaced slits and produces a pattern of bright and dark fringes on a screen (see figure 27.3). The fringe pattern is a direct indication that interference is occurring between the light waves coming from each slit. One of the most incredible discoveries of twentieth‐century physics is that particles can also behave like waves and exhibit interference effects. For instance, figure 29.1 shows a version of Young’s experiment performed by directing a beam of electrons onto a double slit.
- David Prutchi(Author)
- 2012(Publication Date)
- Wiley(Publisher)
Light apparently is something different altogether, but it behaves as a wave when the experiment is designed to reveal its wave-like properties, while it behaves as a particle when the experiment is designed to show its particle-like properties. This schizophrenic personality of light is known as the “wave–particle duality.” The type of experiment will show either light’s particle-like or wave-like behavior, but not both at once, which made Niels Bohr state that the wave and particle aspects of light are complementary to each other. The concept of complementarity derives directly from wave–particle duality, and states that all physical reality is determined and defined by manifestations of properties that are limited by trade-offs between complementary pairs of these properties. MATTER WAVES Even in the light of the Compton Effect, critics of the early single-photon interference experiments dismissed the importance of the observation by noting that a photon doesn’t have mass. Through some fancy hand-waving, they argued that the low-light interference could be caused through splitting and recombining the light quanta’s wavefront. Decisive proof would come when particles with mass would show interference. In 1924, French physicist Prince Louis-Victor de Broglie (pronounced “de Broy,” and by the way, he did belong to the French royalty) proposed that maybe it’s not just light that has this dual personality, maybe it’s everything! He reasoned that if the quanta of light could be both a wave and a particle, then maybe the same could be true of electrons. Remember that although a photon doesn’t have mass, it does have momentum p given by: De Broglie’s hypothesis was that matter—which is commonly described by our perception as “solid”—can also behave as a wave
eBook - PDF- J. Trusted(Author)
- 1999(Publication Date)
- Palgrave Macmillan(Publisher)
The Duality 01 Matter 125 patterns, like those seen with water waves but on a much much smaller scale. Nevertheless scale is immateriali by the end of the first quarter of the twentieth century it was established that elec- tromagnetic waves could behave like particles and that particles could behave like waves. Heisenberg highlights this problem: It was the increased range of technical experience which first forced us to leave the limits of classical concepts. These con- cepts no longer fitted nature as we had come to know it. We observed the track of an electron moving as a particle ... and, on another occasion we found it reflected on a diffraction grating like a wave. The language of classical physics was no longer capable of expressing these two observations as effects of a single entity. We had, first of all, to define more closely those places where classical concepts became ambiguous in their application. 15 Did this mean that all classical concepts of matter were funda- mentally flawed, or was there some hope of reconciling the two approaches, some way of showing that the two accounts described different aspects of some more fundamental reality? One indica- tion that reconciliation might be possible was that the two equations relating momentum and wave length, as given by Compton and de Broglie, connect those same entities, wave length and momentum, through Planck' s constant: Compton p = hll Here we have the relation whereby electromagnetic waves may be treated as moving particles and therefore may be assigned a momentum. And: de Broglie I = hip Here we have the relation whereby moving (orbiting) particles may be treated as waves and therefore may be assigned a wave length. Thus we can say that electromagnetic waves have particle-like properties and sub-atomic particles have wave-like properties. This necessitates removing the common-sense and classical science 126 The Mystery of Matter distinctions between particles and waves.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Focus on Concepts 849 Concept Summary 29.1 The Wave–Particle Duality, 29.2 Blackbody Radiation and Planck’s Constant The wave–particle duality refers to the fact that a wave can exhibit particle-like characteristics and a particle can exhibit wave-like characteristics. At a constant temperature, a perfect blackbody absorbs and reemits all the electromagnetic radiation that falls on it. Max Planck calculated the emitted radiation intensity per unit wavelength as a function of wavelength. In his theory, Planck assumed that a blackbody consists of atomic oscillators that can have only discrete, or quantized, energies. Planck’s quantized energies are given by Equation 29.1, where h is Planck’s constant (6.63 × 10 −34 J · s) and f is the vibration frequency of an oscillator. E = nhf n = 0, 1, 2, 3, . . . (29.1) 29.3 Photons and the Photoelectric Effect All electromagnetic radiation consists of photons, which are packets of energy. The energy of a photon is given by Equation 29.2, where h is Planck’s constant and f is the frequency of the photon. A photon has no mass and always travels at the speed of light c in a vacuum. E = hf (29.2) The photoelectric effect is the phenomenon in which light shining on a metal surface causes electrons to be ejected from the surface. The work function W 0 of a metal is the minimum work that must be done to eject an electron from the metal. In accordance with the conservation of energy, the electrons ejected from a metal have a maximum kinetic energy KE max that is related to the energy hf of the incident photon and the work function of the metal by Equation 29.3. hf = KE max + W 0 (29.3) 29.4 The Momentum of a Photon and the Compton Effect The mag- nitude p of a photon’s momentum is given by Equation 29.6, where h is Planck’s constant and is the wavelength of the photon.
eBook - ePubQuantum Mechanics, Volume 1
Basic Concepts, Tools, and Applications
- Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë(Authors)
- 2020(Publication Date)
- Wiley-VCH(Publisher)
Chapter I Waves and particles. Introduction to the fundamental ideas of quantum mechanics- A Electromagnetic waves and photons
- A-1 Light quanta and the Planck-Einstein relations
- A-2 Wave-Particle Duality
- A-3 The principle of spectral decomposition
- B Material particles and matter waves
- B-1 The de Broglie relations
- B-2 Wave functions. Schrödinger equation
- C Quantum description of a particle. Wave packets
- C-1 Free particle
- C-2 Form of the wave packet at a given time
- C-3 Heisenberg relations
- C-4 Time evolution of a free wave packet
- D Particle in a time-independent scalar potential
- D-1 Separation of variables. Stationary states
- D-2 One-dimensional “square” potentials. Qualitative study
In the present state of scientific knowledge, quantum mechanics plays a fundamental role in the description and understanding of natural phenomena. In fact, phenomena that occur on a very small (atomic or subatomic) scale cannot be explained outside the framework of quantum physics. For example, the existence and the properties of atoms, the chemical bond and the propagation of an electron in a crystal cannot be understood in terms of classical mechanics. Even when we are concerned only with macroscopic physical objects (that is, whose dimensions are comparable to those encountered in everyday life), it is necessary, in principle, to begin by studying the behavior of their various constituent atoms, ions, electrons, in order to arrive at a complete scientific description. Actually, there are many phenomena that reveal, on a macroscopic scale, the quantum behaviour of nature. It is in this sense that it can be said that quantum mechanics is the basis of our present understanding of all natural phenomena, including those traditionally treated in chemistry, biology, etc...From a historical point of view, quantum ideas contributed to a remarkable unification of the concepts of fundamental physics by treating material particles and radiation on the same footing. At the end of the nineteenth century, people distinguished between two entities in physical phenomena: matter and radiation. Completely different laws were used for each one. To predict the motion of material bodies, the laws of Newtonian mechanics (cf. Appendix III) were utilized. Their success, though of long standing, was none the less impressive. With regard to radiation, the theory of electromagnetism, thanks to the introduction of Maxwell’s equations, had produced a unified interpretation of a set of phenomena which had previously been considered as belonging to different domains: electricity, magnetism and optics. In particular, the electromagnetic theory of radiation had been spectacularly confirmed experimentally by the discovery of Hertzian waves. Finally, interactions between radiation and matter
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
29.6 | Calculate quantum uncertainty using the Heisenberg uncertainty principle. 738 Susumu Nishinaga/Science Source 29.2 | Blackbody Radiation and Planck’s Constant 739 in this chapter. For the moment, we intend only to emphasize that the concept of an electron as a tiny discrete particle of matter does not account for the fact that the electron can behave as a wave in some circumstances. In other words, the electron exhibits a dual nature, with both particle-like characteristics and wave-like characteristics. Here is another interesting question: If a particle can exhibit wave-like properties, can waves exhibit particle-like behavior? As the next three sections reveal, the answer is yes. In fact, experiments that demonstrated the particle-like behavior of waves were performed near the beginning of the twentieth century, before the experiments that demonstrated the wave-like properties of the electrons. Scientists now accept the wave–particle duality as an essential part of nature: Waves can exhibit particle-like characteristics, and particles can exhibit wave-like characteristics. Section 29.2 begins the remarkable story of the wave–particle duality by discussing the electromagnetic waves that are radiated by a perfect blackbody. It is appropriate to begin with blackbody radiation, because it provided the first link in the chain of experimental evidence leading to our present understanding of the wave–particle duality. 29.2 | Blackbody Radiation and Planck’s Constant All bodies, no matter how hot or cold, continuously radiate electromagnetic waves. For in- stance, we see the glow of very hot objects because they emit electromagnetic waves in the visible region of the spectrum. Our sun, which has a surface temperature of about 6000 K, appears yellow, while the cooler star Betelgeuse has a red-orange appearance due to its lower surface temperature of 2900 K.
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