Introduction to Quantum Physics

Introduction to Quantum Physics tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩnh...

Introduction to Plasma Physics: A graduate level course Richard Fitzpatrick 1 Associate Professor of Physics The University of Texas at Austin 1 In association with R.D. Hazeltine and F.L. Waelbroeck. Contents 1 Introduction 5 1.1 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 What is plasma? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 A brief history of plasma physics . . . . . . . . . . . . . . . . . . . 7 1.4 Basic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 The plasma frequency . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Debye shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 The plasma parameter . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.8 Collisionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.9 Magnetized plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.10 Plasma beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Charged particle motion 20 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Motion in uniform fields . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Method of averaging . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Guiding centre motion . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 Magnetic drifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Invariance of the magnetic moment . . . . . . . . . . . . . . . . . 31 2.7 Poincar ´ e invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.8 Adiabatic invariants . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.9 Magnetic mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.10 The Van Allen radiation belts . . . . . . . . . . . . . . . . . . . . . 37 2.11 The ring current . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.12 The second adiabatic invariant . . . . . . . . . . . . . . . . . . . . 46 2.13 The third adiabatic invariant . . . . . . . . . . . . . . . . . . . . . 48 2.14 Motion in oscillating fields . . . . . . . . . . . . . . . . . . . . . . . 49 3 Plasma fluid theory 53 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Moments of the distribution function . . . . . . . . . . . . . . . . . 56 3.3 Moments of the collision operator . . . . . . . . . . . . . . . . . . . 58 3.4 Moments of the kinetic equation . . . . . . . . . . . . . . . . . . . 61 2 3.5 Fluid equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.6 Entropy production . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.7 Fluid closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.8 The Braginskii equations . . . . . . . . . . . . . . . . . . . . . . . . 72 3.9 Normalization of the Braginskii equations . . . . . . . . . . . . . . 85 3.10 The cold-plasma equations . . . . . . . . . . . . . . . . . . . . . . 93 3.11 The MHD equations . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.12 The drift equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.13 Closure in collisionless magnetized plasmas . . . . . . . . . . . . . 100 4 Waves in cold plasmas 105 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2 Plane waves in a homogeneous plasma . . . . . . . . . . . . . . . . 105 4.3 The cold-plasma dielectric permittivity . . . . . . . . . . . . . . . . 107 4.4 The cold-plasma dispersion relation . . . . . . . . . . . . . . . . . 110 4.5 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.6 Cutoff and resonance . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.7 Waves in an unmagnetized plasma . . . . . . . . . . . . . . . . . . 114 4.8 Low-frequency wave propagation in a magnetized plasma . . . . Introduction to Quantum Physics Introduction to Quantum Physics Bởi: OpenStaxCollege A black fly imaged by an electron microscope is as monstrous as any science-fiction creature (credit: U.S Department of Agriculture via Wikimedia Commons) 1/3 Introduction to Quantum Physics Quantum mechanics is the branch of physics needed to deal with submicroscopic objects Because these objects are smaller than we can observe directly with our senses and generally must be observed with the aid of instruments, parts of quantum mechanics seem as foreign and bizarre as parts of relativity But, like relativity, quantum mechanics has been shown to be valid—truth is often stranger than fiction Certain aspects of quantum mechanics are familiar to us We accept as fact that matter is composed of atoms, the smallest unit of an element, and that these atoms combine to form molecules, the smallest unit of a compound (See [link].) While we cannot see the individual water molecules in a stream, for example, we are aware that this is because molecules are so small and so numerous in that stream When introducing atoms, we commonly say that electrons orbit atoms in discrete shells around a tiny nucleus, itself composed of smaller particles called protons and neutrons We are also aware that electric charge comes in tiny units carried almost entirely by electrons and protons As with water molecules in a stream, we not notice individual charges in the current through a lightbulb, because the charges are so small and so numerous in the macroscopic situations we sense directly Atoms and their substructure are familiar examples of objects that require quantum mechanics to be fully explained Certain of their characteristics, such as the discrete electron shells, are classical physics explanations In quantum mechanics we conceptualize discrete “electron clouds” around the nucleus Making Connections: Realms of Physics Classical physics is a good approximation of modern physics under conditions first discussed in the The Nature of Science and Physics Quantum mechanics is valid in general, and it must be used rather than classical physics to describe small objects, such as atoms Atoms, molecules, and fundamental electron and proton charges are all examples of physical entities that are quantized—that is, they appear only in certain discrete values and not have every conceivable value Quantized is the opposite of continuous We cannot have a fraction of an atom, or part of an electron’s charge, or 14-1/3 cents, for example Rather, everything is built of integral multiples of these substructures Quantum physics is the branch of physics that deals with small objects and the quantization of various entities, including energy and angular momentum Just as with classical physics, quantum physics has several subfields, such as mechanics and the 2/3 Introduction to Quantum Physics study of electromagnetic forces The correspondence principle states that in the classical limit (large, slow-moving objects), quantum mechanics becomes the same as classical physics In this chapter, we begin the development of quantum mechanics and its description of the strange submicroscopic world In later chapters, we will examine many areas, such as atomic and nuclear physics, in which quantum mechanics is crucial 3/3 An Introduction to GEOMETRICAL PHYSICS R. Aldrovandi & J.G. Pereira Instituto de F´ısica Te´orica State Univers ity of S˜ao Paulo – UNESP S˜ao Paulo — Brazil To our parents Nice, Dina, Jos´e and Tito i ii PREAMBLE: SPACE AND GEOMETRY What stuff’tis made of, whereof it is born, I am to learn. Merchant of Venice The simplest geometrical setting used — consciously or not — by physi- cists in their everyday work is the 3-dimensional euclidean space E 3 . It con- sists of the set R 3 of ordered triples of real numbers such as p = (p 1 , p 2 , p 3 ), q = (q 1 , q 2 , q 3 ), etc, and is endowed with a very special characteristic, a metric defined by the distance function d(p, q) =  3  i=1 (p i − q i ) 2  1/2 . It is the space of ordinary human experience and the starting point of our geometric intuition. Studied for two-and-a-half millenia, it has been the object of celebrated controversies, the most famous concerning the minimum number of properties necessary to define it completely. From Aristotle to Newton, through Galileo and Descartes, the very word space has been reserved to E 3 . Only in the 19-th century has it become clear that other, different spaces could be thought of, and mathematicians have since greatly amused themselves by inventing all kinds of them. For physi- cists, the age-long debate shifted to another question: how can we recognize, amongst such innumerable possible spaces, that real space chosen by Nature as the stage-set of its processes? For example, suppose the space of our ev- eryday experience consists of the same set R 3 of triples above, but with a different distance function, such as d(p, q) = 3  i=1 |p i − q i |. This would define a different metric space, in principle as good as that given above. Were it only a matter of principle, it would be as good as iii iv any other space given by any distance function with R 3 as set point. It so happens, however, that Nature has chosen the former and not the latter space for us to live in. To know which one is the real space is not a simple question of principle — something else is needed. What else? The answer may seem rather trivial in the case of our home space, though less so in other spaces singled out by Nature in the many different situations which are objects of physical study. It was given by Riemann in his famous Inaugural Address 1 : “ those properties which distinguish Space from other con- ceivable triply extended quantities can only be deduced from expe- rience.” Thus, from experience! It is experiment which tells us in which space we actually live in. When we measure distances we find them to be independent of the direction of the straight lines joining the points. And this isotropy property rules out the second proposed distance function, while admitting the metric of the euclidean space. In reality, Riemann’s statement implies an epistemological limitation: it will never be possible to ascertain exactly which space is the real one. Other isotropic distance functions are, in principle, admissible and more experi- ments are necessary to decide between them. In Riemann’s time already other geometries were known (those found by Lobachevsky and Boliyai) that could be as similar to the euclidean geometry as we might wish in the re- stricted regions experience is confined to. In honesty, all we can say is that E 3 , as a model for our ambient space, is strongly favored by present day experimental evidence in scales ranging from (say) human dimensions down to about 10 −15 cm. Our knowledge on smaller scales is limited by our ca- pacity to probe them. For larger scales, according to General Relativity, the validity of this model depends on the presence and strength of gravitational fields: E 3 is good only as long as gravitational fields are very weak. “ These data are — like all data — not logically necessary, but only of empirical [...]... programming language Programming languages can be divided into two major categories: low-level languages designed to work with the given hardware, and high-level languages that are not related to any specific hardware Simple machine languages and assembly languages were the only ones available before the development of high-level languages A machine language is typically in binary form and is designed to work... computing and global computing is elucidated in Koniges (2000), Foster and Kesselman (2003), and Abbas (2004) 1.1 Computation and science Modern societies are not the only ones to rely on computation Ancient societies also had to deal with quantifying their knowledge and events It is interesting to see how the ancient societies developed their knowledge of numbers and calculations with different means and tools... of programming and debugging They are more advanced than machine languages because they have adopted symbolic addresses But they are still related to a certain architecture and wiring of the system A translating device called an assembler is needed to convert an assembly code into a native machine code before a computer can recognize the instructions Machine languages and assembly languages do not... discussion on the Fortran language and its applications, see Edgar (1992) The newest version of Fortran, known as Fortran 90, has absorbed many important features for parallel computing Fortran 90 has many extensions over the standard Fortran 77 Most of these extensions are established based on the extensions already adopted by computer manufacturers to enhance their computer performance Efficient compilers... programming languages that are used in scientific computing The longest-running candidate is Fortran (Formula translation), which was introduced in 1957 as one of the earliest high-level languages and is still one of the primary languages in computational science Of course, the Fortran language has evolved from its very early version, known as Fortran 66, to Fortran 77, which has been the most popular language... replace human beings in this regard and the quest for a better understanding of Nature will go on no matter how difficult the journey is Computers will certainly help to make that journey more colorful and pleasant 1.3 Computer algorithms and languages Before we can use a computer to solve a specific problem, we must instruct the computer to follow certain procedures and to carry out the desired computational. .. protocols and environments under various software packages, which we will leave to the readers to discover and explore 1.3 Computer algorithms and languages The other popular programming language for scientific computing is the C programming language Most system programmers and software developers prefer to use C in developing system and application software because of its high flexibility (Kernighan and... (Kernighan and Pike, 1984) now used on almost all workstations and supercomputers was initially written in C In the last 50 years of computer history, many programming languages have appeared and then disappeared for one reason or another Several languages have made significant impact on how computing tasks are achieved today Examples include Cobol, Algol, Pascal, and Ada Another object-oriented language... speed of the motorcycle is 67 m/s, the air density is ρ = 1.2 kg/m3 , the combined mass of the motorcycle and the person is 250 kg, and the coefficient c is 1, find the tilting angle of the taking-off ramp that can produce the longest range 1.9 One way to calculate π is by randomly throwing a dart into the unit square defined by x ∈ [0, 1] and y ∈ [0, 1] in the x y plane The chance of the dart landing inside... efficient approach to learning computational physics is .. .Introduction to Quantum Physics Quantum mechanics is the branch of physics needed to deal with submicroscopic objects Because these objects... and angular momentum Just as with classical physics, quantum physics has several subfields, such as mechanics and the 2/3 Introduction to Quantum Physics study of electromagnetic forces The correspondence... of modern physics under conditions first discussed in the The Nature of Science and Physics Quantum mechanics is valid in general, and it must be used rather than classical physics to describe