Physics
Quantum Physics Basics
Quantum physics is a branch of physics that deals with the behavior of particles at the atomic and subatomic levels. It introduces the concept of quantization, where certain physical quantities, such as energy and momentum, are restricted to discrete values. Quantum physics also encompasses the wave-particle duality, which describes how particles can exhibit both wave-like and particle-like properties.
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12 Key excerpts on "Quantum Physics Basics"
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- Andrew Zimmerman Jones(Author)
- 2024(Publication Date)
- For Dummies(Publisher)
2 The Fundamentals: Quantum Physics Principles and Theories IN THIS PART . . . Find out what quantum physics says about particle states. Look back at how quantum physics has revolutionized our understanding of electromagnetism and matter. Investigate the central interpretations, contradictions, and debates of quantum physics. CHAPTER 4 Quantum Mechanics: Particle States and Dualities 71 Chapter 4 Quantum Mechanics: Particle States and Dualities I n the field of quantum physics, you tend to look at individual particles and how those particles behave. (You dive a little bit into multiple particle systems in Chapter 15.) At the core of your examination is understanding that quantum physics defines individual particles in terms of their particle states. Suppose that you have a particle that is in a certain state at one point; examining the particle further means you look at the likelihood that the particle will be in certain other states at other points. In this chapter, you find out about quantum states of particles. I start with an explanation of the quantum numbers that physicists use to describe quantum states, and some specific ways those states manifest in physics. Then I return to an idea, introduced in Chapter 3, of wave-particle duality, which is central to quantum physics. Finally, I talk a bit about how quantum physics led physicists to predict and then discover antimatter. IN THIS CHAPTER » Exploring the role of quantum numbers » Learning how spin defines particles » Diving deeper into wave-particle duality » Identifying the nature of antimatter 72 PART 2 The Fundamentals: Quantum Physics Principles and Theories Quantifying by Quantum Numbers Particles in quantum physics are in defined states, and these states are repre- sented by a sequence of numbers. The numbers that quantum physicists use to define a quantum state are called quantum numbers. Niels Bohr first used this approach when he developed the Bohr model of the atom, as described in Chapter 3.
- 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- Ashok Das(Author)
- 2012(Publication Date)
- WSPC(Publisher)
Chapter 3 Basics of quantum mechanics In the next few lectures, we will introduce the basic concepts of quan-tum mechanics. However, let us first discuss the reasons for going beyond the classical description of physical systems, which we have discussed in the first chapter. 3.1 Inadequacies of classical mechanics Classical mechanics works well when applied to macroscopic or large systems. However, around the turn of the twentieth century (1900-1920), it was observed that microscopic or small systems behaved very differently from the predictions of classical mechanics. We would, of course, discuss more quantitatively what we mean by microscopic systems. But, for the present, let us understand by a microscopic system, a system of atomic size or smaller and list below various difficulties that one runs into in applying the classical description to microscopic systems. 1. Planetary model. The planetary model of the atom, where elec-trons move in definite orbits around the nucleus, was in serious trouble. According to classical mechanics, a particle in such an orbit is being constantly accelerated. Furthermore, we also know that a classical charged particle, when accelerated, emits radiation. Therefore, an electron going around a nucleus would continuously emit radiation and become less and less energetic. This has the consequence that the radius of the orbit would con-stantly shrink in size, until the electron falls into the nucleus. Thus, according to classical mechanics, the planetary motion in atoms was unstable. 2. Blackbody radiation. The theoretical calculation of the black-body radiation spectrum, which assumes that electromagnetic radiation is a wave and, therefore, can exchange energy in any 61 62 3 Basics of quantum mechanics continuous amount, leads to a result which does not agree with the experimental measurement (curve).
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 - 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
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.
eBook - PDF- Vishnu S. Mathur, Surendra Singh(Authors)
- 2008(Publication Date)
- Chapman and Hall/CRC(Publisher)
1 NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS 1.1 Inadequacy of Classical Description for Small Systems Classical mechanics, which gives a fairly accurate description of large systems (e.g., solar system) as also of mechanical systems in our every day life, however, breaks down when applied to small (microscopic) systems such as molecules, atoms and nuclei. For example, (1) classical mechanics cannot even explain why the atoms are stable at all. A classical atom with electrons moving in circular or elliptic orbits around the nucleus would continuously radiate energy in the form of electromagnetic radiation because an accelerated charge does radiate energy. As a result the radius of the orbit would become smaller and smaller, resulting in instability of the atom. On the other hand, the atoms are found to be remarkably stable in practice. (2) Another fact of observation that classical mechanics fails to explain is wave particle duality in radiation as well as in material particles. It is well known that light exhibits the phenomena of interference , diffraction and polarization which can be easily understood on the basis of wave aspect of radiation. But light also exhibits the phenomena of photo-electric effect , Compton effect and Raman effect which can only be understood in terms of corpuscular or quantum aspect of radiation. The dual behavior of light, or radiation cannot be consistently understood on the basis of classical concepts alone or explained away by saying that light behaves as wave or particle depending on the kind of experiment we do with it (complementarity). Moreover, a beam of material particles, like electrons and neutrons, demonstrates wave-like properties (e.g., diffraction). A brief outline of phenomena that require quantum mechanics for their understanding follows.
- Tian Yu Cao(Author)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
We must refrain from determining the amount of momentum that passes into the instrument in order to apply the space-time point of view” (Bohr, 1928). 124 The Rise of Quantum Theory 7 The Formation of the Conceptual Foundations of Quantum Field Theory Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual scheme, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated carefully; no detailed discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest. The content of this chapter involves the formation and interpretation, in a roughly chronological order, of the concepts of the wave function, quantization (of energy or of the electromagnetic field), quantum field, the vacuum, interactions between fields, and renormalization. The first two topics will be discussed in relation to the discovery of the quantum field and its various representations, which was the starting point of the concep- tual development of QFT. As to interactions, which were the origin of field theories (classical as well as quantum) and the main subject of this volume, in addition to a brief treatment given here, further discussions will be given in Part III. 7.1 The Tortuous Route to the Quantum Field Quantum field theory is not a quantum theory applied to classical fields. Rather, it is a theory of quantum fields. Quantum fields belong to a new natural kind, categorically different from the old natural kind of classical fields. The recognition of quantum fields as such was achieved through a complicated constructive process rife with confusions and misinterpretations.
eBook - PDF- Noson S. Yanofsky, Mirco A. Mannucci(Authors)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
2 No attempt will be made to present the material in an exhaustive historical manner. The curious reader can refer to the references at the end of this chapter for a plethora of good, comprehensive introduc- tions to quantum mechanics. 103 104 Basic Quantum Theory Figure 4.1. Young’s double-slit experiment. ultimately composed of microscopic particles, and light was thought of as continuous electromagnetic waves propagating in space. The dichotomy – particles versus waves – was proven false by several ground- breaking experiments. For instance, the diffraction experiment shows that a beam of subatomic particles hitting a crystal diffract following a wave-like pattern, en- tirely similar to the diffraction pattern of light itself. By the mid-twenties, physicists started associating waves to all known particles, the so-called matter waves (the first proposal was made by French physicist Louis De Broglie in 1924 in his doctoral dissertation). The photoelectric effect (observed by Hertz in 1887) showed that an atom hit by a beam of light may absorb it, causing some electrons to transition to a higher- energy orbital (i.e., farther from the nucleus). Later on, the absorbed energy may be released in the form of emitted light, causing the excited electrons to revert to a lower orbital. What the photoelectric effect unraveled was that light-matter trans- actions always occur through discrete packets of energy, known as photons (the concept was introduced by Einstein in his seminal 1905 paper, as a way to account for the photoelectric effect). Photons act as genuine particles that can get absorbed and emitted, one at a time. Further experimental evidence from many quarters accumulated over time, strongly suggesting that the old duality particle–wave theory must be replaced by a new theory of the microscopic world in which both matter and light manifest a particle-like and a wave-like behavior. Time was ripe for the conceptual framework of quantum mechanics.
eBook - PDFQuantum Mechanics
Foundations and Applications
- Donald Gary Swanson(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
1 The Foundations of Quantum Physics 1.1 The Prelude to Quantum Mechanics Quantum mechanics is essentially a 20th century development that is based on a number of observations that defied classical explanations. While some of these experiments have semiclassical explanations, the triumph of quantum mechanics is that it gives precise verification for an overwhelming number of experimental observations. Its extensions into relativistic quantum mechanics through quantum electrodynamics (QED), electro-weak theory, and quantum chromodynamics (QCD) have led us to the Standard Model of today. While the number of unanswered questions remains approximately constant at each stage of development, the number of answered questions that relate theory with experiment continues to grow rapidly. In this chapter, some of the historical landmarks in the development of the theory are noted. The resolution of the dilemmas presented by classical theory will be dealt with in later chapters, but these are listed to motivate the break from classical mechanics. Because of the apparently unphysical nature of the postulates upon which quantum mechanics is founded, we supply motivation and justification for this break. In the first part of this chapter, we will review some of the experiments that confounded classical theory, and then introduce a formalism that provides some rationale for the postulates upon which quantum mechanics is based. In the end, these postulates will stand on their own. 1.1.1 The Zeeman Effect Looking back to the last few years of the 19th century, the discovery by J.J. Thomson of the electron in 1897 was followed almost immediately by the an-nouncement from Zeeman and Lorentz that it participated in electromagnetic radiation from atoms.
eBook - PDF- Gennaro Auletta, Mauro Fortunato, Giorgio Parisi(Authors)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
P A R T I BASIC FEATURES OF QUANTUM MECHANICS 1 From classical mechanics to quantum mechanics In this chapter we shall first summarize some conceptual and formal features of classical mechanics (Sec. 1.1 ). Modern physics started with the works of Galileo Galilei and Isaac Newton from which classical mechanics, one of the most beautiful and solid intellectual buildings of the human history, came out. The architecture of classical mechanics was developed between the end of the eighteenth century and the second half of the nineteenth century, and its present form is largely due to Lagrange, Jacobi, and Hamilton. As we shall see in this chapter, classical mechanics is built upon the requirement of determinism, a rather complex assumption which is far from being obvious. In Sec. 1.2 we shall present the two main conceptual features of quantum mechanics on the basis of an ideal inter-ferometry experiment: the superposition principle and the principle of complementarity. In Sec. 1.3 a first formal treatment of quantum-mechanical states is developed: quantum states are represented by vectors in a space that turns out to be a Hilbert space. In Sec. 1.4 the significance of probability for quantum mechanics is explained briefly: we will show that probability is not just an ingredient of quantum mechanics, but is rather an intrin-sic feature of the theory. Furthermore, we shall see that quantum probability is not ruled by Kolmogorov axioms of classical probability. Finally, we discuss the main evidences which have historically revealed the necessity of a departure from classical mechanics. Our task then is to briefly present the principles upon which quantum mechanics is built (in Secs. 1.2 – 1.4 ) and to summarize in Sec. 1.5 the main evidences for this new mechanics. 1.1 Review of the foundations of classical mechanics Classical mechanics is founded upon several principles and postulates, sometimes only implicitly assumed.
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