Physics
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the atomic and subatomic levels. It introduces the concept of quantized properties, such as energy and angular momentum, and provides a framework for understanding phenomena like wave-particle duality and quantum entanglement. The theory has profound implications for our understanding of the nature of reality at the smallest scales.
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12 Key excerpts on "Quantum Mechanics"
eBook - PDFThe Sciences
An Integrated Approach
- James Trefil, Robert M. Hazen(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
234 CHAPTER 9 How can the electron behave like both a particle and a wave? Quantum Mechanics GREAT IDEA At the subatomic scale, everything is quantized. Any measurement at that scale significantly alters the object being measured. TECHNOLOGY Sensitive electronic detectors can detect the emission of a single photon from an excited atom. PHYSICS Quantum Mechanics requires an entirely new way of describing the state of a system at the level of the atom. BIOLOGY Some scientists think that Quantum Mechanics is intimately involved in the phenomenon of consciousness. ASTRONOMY The nuclear reactions that power the Sun are governed by the laws of Quantum Mechanics. (Ch. 14) CHEMISTRY Wave-particle duality explains the shapes of allowed electron orbits, and therefore the chemical reactions of atoms. HEALTH & SAFETY In CAT scans, photoelectric devices convert X-ray photons into electrical currents, whose strength can be used to produce a picture of a patient’s internal organs. GEOLOGY The way that atoms combine to form minerals is governed by the laws of Quantum Mechanics. = applications of the great idea discussed in this chapter = other applications, some of which are discussed in other chapters 9.1 | The World of the Very Small 235 9.1 The World of the Very Small In Chapter 8, we saw that when an electron moves between energy levels and emits a photon, it is said to make a quantum leap. The term Quantum Mechanics refers to the theory that describes this event and other events at the scale of the atom. The word quantum comes from the Latin word for “bundle,” and mechanics, as we saw in Chapter 2, is the study of the motion of material objects. Quantum Mechanics, then, is the branch of science that is devoted to the study of the motion of objects that come in small bundles, or quanta. We have already seen that material inside the atom comes in little bundles—tiny pieces of matter we call electrons travel in orbits around another little bundle of matter we call the nucleus.
eBook - PDF- Andrew Zimmerman Jones(Author)
- 2024(Publication Date)
- For Dummies(Publisher)
In this chapter, you see how physicists throughout the middle of the twentieth century explained the structure of matter and energy (almost entirely) in terms of quantum physics. You find out about some of the inventions that came out of the quantum revolution — inventions that are so ubiquitous now that most people don’t even realize how much they rely on them. Then you take a look at something that feels like science fiction: the amazing possibility of quantum computing. IN THIS CHAPTER » Seeing how quantum physics explains the fundamental forces » Exploring the inventions derived from quantum physics » Looking at the possibilities of quantum computing 78 PART 2 The Fundamentals: Quantum Physics Principles and Theories Quantum Field Theory: Explaining Matter and Energy Quantum physics studies brought about amazing achievements throughout the middle of the twentieth century and explained (at the most fundamental level) nearly everything about matter and energy. In Chapter 2, I describe classical physics ideas that took centuries to understand and refine. In the span of a few decades — starting when Max Planck first proposed quantizing physical proper- ties in 1900 (see Chapter 3 for more about this proposal) — physicists used Planck’s idea to explain the nature of electromagnetism, as well as the forces that held atoms together! The foundation of these revolutionary ideas was quantum field theory, an approach to quantum physics that uses the concept of fields. A field in physics is a model where space is filled with a physical quantity that has a value at each point in space and time. If the field also has a direction, it’s called a vector field. (Check out Chapters 2 and 3 for more about fields.) Quantum field theory defines quantum physics in terms of a quantum field that permeates all space and has energy (a scalar or magnitude) and momentum (a vec- tor with both magnitude and direction) throughout space and time.
eBook - PDF- Md Nazoor Khan, Simanchala Panigrahi(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
7 Elementary Concepts of Quantum Physics 7.1 Introduction It is correctly told that mathematics is the queen of all sciences; in the same spirit, quantum physics or Quantum Mechanics may be called the king of all sciences. Our knowledge in any field of science is incomplete as long as we remain unacquainted with quantum physics. The concepts of quantum physics form the basis for our present understanding of physical phenomena on an atomic and microscopic scale. The concepts of quantum physics can be applied to most fields of science and engineering starting from biology to quantum computers to cosmology. Within engineering, important subjects of practical significance include semiconductor transistors, lasers, quantum optics, and molecular devices where quantum physics plays the most vital role. As technology advances, quantum concepts give birth to an increasing number of new electronic and opto-electronic devices. Their fabrications and functions can only be understood by using quantum physics. Within the next few years, fundamentally quantum devices such as single-electron memory cells and photonic signal processing systems may be available commercially. As nano-and atomic-scale devices become easier to manufacture, these sophisticated manufacturing units will require an increasing number of individuals with sound knowledge of quantum physics. Therefore, all universities in the world have included quantum physics as a subject in their technical course curricula. Quantum physics is no longer a theoretical subject with mathematical complexities but an engineering subject! 7.2 Need for Quantum Physics Two time-tested proverbs are, ‘Failure is the pillar of success' and 'Necessity is the mother of invention’. Classical physics based on Newtonian laws, thermodynamical laws and 550 Principles of Engineering Physics 1 classical laws of electromagnetism explained successfully the macroscopic world.
eBook - PDF- Ian D. Lawrie(Author)
- 2012(Publication Date)
- CRC Press(Publisher)
While the mathemati- cal developments that constitute Quantum Mechanics have been outstandingly successful in describing all manner of observed properties of matter, it is fair to say that the conceptual basis of the theory is still somewhat obscure. I my- self do not properly understand what it is that quantum theory tells us about the nature of the physical world, and by saying this I mean to imply that I do not think anybody else understands it either, though there are respectable scientists who write with confidence on the subject. This need not worry us unduly. There does exist a canon of generally accepted phrases which, if we do not examine them too critically, provide a reliable means of extracting from the mathematics well defined predictions for the outcome of any experiment we can perform (apart, that is, from the difficulty of solving the mathemat- ical equations, which can be very great). I shall generally use these without comment, and readers must choose for themselves whether or not to accept them at face value. This chapter deals with non-relativistic Quantum Mechanics, and I am go- ing to assume that readers are already familiar with the more elementary 141 142 A Unified Grand Tour of Theoretical Physics aspects of the subject. The following section outlines the reasons why clas- sical mechanics has proved inadequate and reviews the elementary ideas of wave mechanics. Although the chapter is essentially self-contained, readers who have not met this material before are urged to consult a textbook on Quantum Mechanics for a fuller account. The remaining sections develop the mathematical theory in somewhat more general terms, and this provides a point of departure for the quantum field theories to be studied in later chap- ters. 5.0 Wave Mechanics The observations which led to the quantum theory are often summarized by the notion of particle–wave duality.
The description of particles in terms of a wave defies our com- monsense. Situations in which a photon or an electron seems to “know” how an appa- ratus will be arranged before the arranging is done seem wrong and unnatural. Many people, scientists and nonsci- entists alike, find the conclusions of quan- tum mechanics to be quite unsettling. The American physicist Richard Feynman stressed this point when he said, “I can safely say that nobody understands quan- tum mechanics. . . . Do not keep saying to yourself, ‘But how can it be like that?’ . . . Nobody knows how it can be like that.” In spite of this rather disturbing situ- ation, the success of Quantum Mechanics provides ample evidence that there is a cor- rect way to describe an atomic-scale system. If you ignore this fact, you can get into a lot of trouble. Newtonian notions like position and velocity just aren’t appropri- ate for the quantum world, which must be described from the beginning in terms of waves and probabilities. Quantum mechan- ics thus becomes a way of predicting how subatomic objects change in time. If you know the state of an electron now, you can use Quantum Mechanics to predict the state of that electron in the future. This process is identical to the application of Newton’s laws of motion in the macroscopic world. The only difference is that in the quantum world, the “state” of the system is a probability. In the view of most working scientists, Quantum Mechanics is a marvelous tool that allows us to do all sorts of experiments and build all manner of new and important pieces of equipment. The fact that we can’t visualize the quantum world in familiar terms seems a small price to pay for all the benefits we receive. TECHNOLOGY Quantum Computing Computers have become a common tool in everyday life—you probably use one rou- tinely in your schoolwork.
eBook - PDF- David Z Albert, David Z. ALBERT(Authors)
- 2009(Publication Date)
- Harvard University Press(Publisher)
▲▲▲ Notwithstanding the profound violence all this does to our earlier pic-ture of the world, to the very idea of what it is to be material, to be a particle, a compact set of rules has been cooked up (a set of rules which is called quan-tum mechanics ) which has proven extraordinarily successful at predicting all of the thus-far-observed behaviors of electrons under the circumstances we have just been talking about, and which (as a matter of fact) has proven ex-traordinarily successful at predicting all of the thus-far-observed behaviors of Quantum Mechanics 139 all physical systems under all circumstances, and which has functioned for more than seventy years now (as everybody knows) as the framework within which the entirety of the enterprise of theoretical physics is carried out. Now, the mathematical object with which Quantum Mechanics repre-sents both the instantaneous states and the full dynamical conditions of physical systems (which amount to one and the same thing —remember— for quantum-mechanical systems) is called the wave-function. Representing things that way (according to Quantum Mechanics) represents them com-pletely, which is to say that absolutely everything that’s the case about any given physical system at any given temporal instant (that is, the value of every single physical property of that system whose value there is—at that instant—any determinate matter of fact about, and the probability of any particular outcome of, any particular measurement one might choose to carry out on that system at that instant, whether there is at the present instant any matter of fact about the value of the property to be measured or not ) can be read off (according to Quantum Mechanics) from its wave-function. In the particularly simple case of a single-particle system of the sort we’ve been concerned with over the last few pages, the quantum-mechanical wave-function takes the form of a straightforward function of (among other things) position in space.
eBook - PDF- Ravinder R. Puri(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
CHAPTER 1 History of Quantum Mechanics History is the most fundamental science, for there is no human knowledge which cannot lose its scientic character when men forget the conditions under which it originated, the questions it answered, and the functions it was created to serve. A student of Quantum Mechanics can ignore these words of Benjamin Farrington, often quoted by Schrödinger [1], only at his own peril. For, without their historical perspective, the counter-intuitive nature of the physical laws of the quantum theory may appear to be mystic. Indeed, the laws of Quantum Mechanics exhibit their distinctive character on a scale which is out of reach of our everyday experience. This is in contrast with the intuitive appeal of the Newton’s laws and their conformity with our common experience. However, the inability of the then known theories, referred to now as the classical theories, to explain certain physical phenomena led to the search for a new theory. It culminated with the advent of the quantum theory. The true scientic character of the quantum theory cannot be appreciated without understanding the conditions under which it originated, the questions it answered, and the functions it was created to serve. Such an understanding can even motivate one to ponder whether there can be any other description of the laws of nature which is free from the conceptual and philosophical inconsistencies which are often pointed out in the present-day quantum theory. This chapter outlines briey how the ideas leading to the birth of Quantum Mechanics took shape. 1.1 Failure of Classical Physics A comprehensive account of history of the quantum theory can be found in several books (for example [2]–[4]).
eBook - PDF- Mikio Namiki, Saverio Pascazio, Hiromichi Nakazato(Authors)
- 1998(Publication Date)
- World Scientific(Publisher)
Chapter 2 ELEMENTS OF Quantum Mechanics We briefly review some fundamental ideas and techniques of quantum mechan-ics that are necessary to discuss the quantum measurement problem. 1 Wave-particle dualism Experiments tell us that a quantum mechanical particle has both the wave and particle nature: This is called wave-particle dualism. The particle is a wave in the sense of showing interference phenomena, and is a particle by virtue of its characteristic of being an indivisible entity. The wave nature (specified by wave number k and frequency u>) and the particle nature (specified by momentum p and energy E) are related to each other by the de Broglie relations k = l w = f, (2.1) h = 1.054 x 10 _34 Js being the Planck constant. Remember that the wave-particle dualism is an experimental fact, which, is indispensable and sufficient to construct the whole theory of Quantum Mechanics. 1.1 Experimental facts The wave nature is brought to light by an interference experiment, for example, of the Young type. Look again at Fig. 1.3. The incident wave ^o is decomposed, by the double slit barrier, into two branch waves, ^> a and V'b, which are then superposed as in ipi of (1.10) downstream from the barrier. Finally, we observe the particle intensity, proportional to (1.11), on a remote screen. The last term in the r.h.s. of (1.11) is called the interference term. The surface of the screen is covered with a large number of small detectors, by which we can observe the particle distribution as given by (1.11). (For the position measurement on the screen, refer to the discussion in Sections 1.2 in Chapter 1 and 2.2 in Chapter 4.) Needless to say, if we observe a beautiful interference 25 26 Elements of QM pattern (as shown by P in Fig. 1.3) on the screen, we can conclude that the particle discloses its wave nature. The wave nature of quantum mechanical particles was recognized in this way.
- Chary Rangacharyulu, Emmanuel Haven(Authors)
- 2010(Publication Date)
- World Scientific(Publisher)
The same holds true for the laser and the light-emitting diode, which jointly provide the basis for optical communication networks (the backbone of the telecommunications industry) and optical data storage (in the form of CDs and DVDs, for example), and many other 204 technologies. Yet more quantum technology (such as quantum computers and quantum cryptography) is waiting in the wings, promising to transform our lives still further. The empirical successes of quantum theory leave little doubt that the mathematical rules of quantum theory—the quantum formalism — accurately capture fundamental features of the workings of the physical world. Since their formulation over 80 years ago, there have been very strong indications that these rules describe a physical reality that cannot be encompassed within the view of reality that underpins classical physics. However, the precise nature of the implications of the quantum formalism for our understanding of the material world remains obscure. 2. Classical Physics and the Nature of a Physical Theory To understand better the nature of the problem and its importance, it is helpful to begin by considering classical physics. Underlying classical physics is a definite conception of the nature of reality, which traces back to the pioneering work of such figures as Descartes, Galileo, and Newton in the seventeenth century. The essential idea is that the totality of all that exists in the phenomenal world (namely that aspect of the world registered by our senses or instrumental extensions thereof such as microscopes or telescopes) is matter moving on the fixed stage of space in step with a universal time in precise accord with mathematical, deterministic laws of motion.
eBook - PDF- Yuri A Berezhnoy(Author)
- 2005(Publication Date)
- WSPC(Publisher)
Chapter 1 Quantum Mechanics 1.1 Why Two Types of Mechanics? We live in a complicated world. Our sense organs provide a steady flow of information regarding the numerous phenomena that surround us. Powerful technological inventions also extend the reach of the human senses, giving us access to information more exact and complete than would otherwise be available. The world of our sense perception is the macroscopic one. Here phys-ical phenomena are described by classical physics, which includes classical mechanics, continuum mechanics (hydrodynamics and the theory of elastic-ity), thermodynamics, and electrodynamics. Because classical physics deals with phenomena in which microscopic structure plays no significant role, it cannot yield a comprehensive theory of the structure of real substances. The laws of classical physics govern the motions of objects whose linear dimensions are sufficiently large: R c > 10 6 m, say. Nothing more powerful than an optical microscope will be needed to observe such objects. Classical mechanics, in particular, describes the motions of planets, comets, stars, and galaxies. But there exists another world, inaccessible to direct observation through our sense organs. This is the amazing world of micro-objects, in which physical phenomena are subject to the laws of quantum mechan-ics. The dimensions of molecules, atoms, atomic nuclei, and elementary particles are very small and could be characterized as -R qu < 1(T 8 m. l 2 The Quantum World of Nuclear Physics Thus we have two distinct physical theories. One describes macroscopic phenomena, the other microscopic phenomena. Why do two types of me-chanics exist? The answer is far from simple. Let us pursue the question in more detail. Until the end of the 19th century, practically all physical phenomena were described using classical mechanics. This subject was originally ex-pounded by Sir Isaac Newton in his Philosophiae naturalis principia math-ematica, a monumental work published in 1687.
eBook - PDFFundamental Principles of Modern Theoretical Physics
International Series of Monographs in Natural Philosophy
- R. H. Furth, D. Ter Haar(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
PART I Quantum Theory This page intentionally left blank CHAPTER 1 The Fundamental Principles of Classical Physics ALTHOUGH, as explained in the introduction, the fundamental principles of quantum theory are in many respects different from those of classical phy-sics and the quantum laws are formulated differently from the classical laws, quantum theory has, nevertheless, grown organically from classical theory. It was therefore considered to be necessary to give in this chapter first a brief review of the main methods employed in classical physics to an extent to which they will subsequently be needed. 1.1. Discontinuum or particle theory In the discontinuum or particle theories it is assumed that material physical systems 1111 space discontinuously, being built up of particles which, on any observable scale, are so small that their position in space is completely determined by a position vector r with respect to a suitable system of co-ordinates.t The state variables of a closed system are therefore identical with the position vectors r i and the velocity vectors n i = i i of all its constituent particles. The particles are acted upon by forces F i which are partly external, having their origin outside the system, and partly internal, acting between the particles. The task of the theory is to set up equations between the coordin-ates, the forces, and the time which make it possible to determine the motion of the particles at any time when the state of the system at time t = O is given. In Newtonian dynamics the equations of motion have the form m i i i = m i ll i = F i (i = 1, 2, ..., N) (1.1.1) where m i is the (constant) mass of the ith particle, F i the force on this particle, which in general is a function of the position and velocity of that particle and may also depend on the positions and velocities of the other t Throughout this book vectors will always be denoted by symbols in heavy type. 3
- Malin Premaratne, Govind P. Agrawal(Authors)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
2 Quantum-Mechanical Framework Quantum Mechanics is not a theory about reality, it is a prescription for making the best possible predictions about the future if we have certain information about the past. G. ’t Hooft, Journ. Stat. Phys. 53, 323 (1988) 2.1 Review of Classical Mechanics A mathematical description of a nanoscale device is typically based on the equations of motion describing how different parts making up the device change with time [70]. Such a description depends heavily on our understanding of the laws governing the device and on the approximations adopted in formulating the equations of motion. For example, a single device could have different equations of motion, depending on whether we use Newtonian mechanics, Quantum Mechanics, or relativistic mechanics to describe it [71]. So, one may ask whether a single set of equations of motion can be used if one agrees in advance on the physics describing the device. The answer is clearly no, because the equations of motion change with the type of coordinates used for locating various parts of a system relative to an agreed reference point (the origin of the coordinate axes). The only requirement for such coordinates is that they should be sufficiently unique to identify each and every part of a device. 2.1.1 Generalized Coordinates The coordinates used in classical mechanics are referred to as generalized coordinates [72, 73]. As different choices of generalized coordinates result in different equations of motion for the same device, the equations of motion for any device are not unique. The situation is further complicated because specific properties of the components, referred to as the constitutive relations, are required to thread the physical laws governing the constraints restricting motion of the device [74].
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