An Introduction To The Uncertainty Principle
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An Introduction To The Uncertainty Principle
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Author : Sundaram Thangavelu
language : en
Publisher: Birkhäuser
Release Date : 2003-10-09
An Introduction To The Uncertainty Principle written by Sundaram Thangavelu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with Mathematics categories.
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.
The Uncertainty Principle In Harmonic Analysis
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Author : Victor Havin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Uncertainty Principle In Harmonic Analysis written by Victor Havin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).
An Introduction To Uncertainty In Measurement
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Author : L. Kirkup
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-01
An Introduction To Uncertainty In Measurement written by L. Kirkup and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-01 with Science categories.
Measurement shapes scientific theories, characterises improvements in manufacturing processes and promotes efficient commerce. In concert with measurement is uncertainty, and students in science and engineering need to identify and quantify uncertainties in the measurements they make. This book introduces measurement and uncertainty to second and third year students of science and engineering. Its approach relies on the internationally recognised and recommended guidelines for calculating and expressing uncertainty (known by the acronym GUM). The statistics underpinning the methods are considered and worked examples and exercises are spread throughout the text. Detailed case studies based on typical undergraduate experiments are included to reinforce the principles described in the book. This guide is also useful to professionals in industry who are expected to know the contemporary methods in this increasingly important area. Additional online resources are available to support the book at www.cambridge.org/9780521605793.
The Physical Principles Of The Quantum Theory
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Author : Werner Heisenberg
language : en
Publisher: Courier Corporation
Release Date : 2013-04-15
The Physical Principles Of The Quantum Theory written by Werner Heisenberg and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Science categories.
Nobel Laureate discusses quantum theory, uncertainty, wave mechanics, work of Dirac, Schroedinger, Compton, Einstein, others. "An authoritative statement of Heisenberg's views on this aspect of the quantum theory." — Nature.
An Introduction To The Uncertainty Principle
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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
An Introduction To The Uncertainty Principle written by Sundaram Thangavelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with Mathematics categories.
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.
Principles Of Uncertainty
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Author : Joseph B. Kadane
language : en
Publisher: CRC Press
Release Date : 2020-11-25
Principles Of Uncertainty written by Joseph B. Kadane and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.
Praise for the first edition: Principles of Uncertainty is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. ... the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. ... A must-read for sure!—Christian Robert, CHANCE It's a lovely book, one that I hope will be widely adopted as a course textbook. —Michael Jordan, University of California, Berkeley, USA Like the prize-winning first edition, Principles of Uncertainty, Second Edition is an accessible, comprehensive text on the theory of Bayesian Statistics written in an appealing, inviting style, and packed with interesting examples. It presents an introduction to the subjective Bayesian approach which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. This new edition has been updated throughout and features new material on Nonparametric Bayesian Methods, the Dirichlet distribution, a simple proof of the central limit theorem, and new problems. Key Features: First edition won the 2011 DeGroot Prize Well-written introduction to theory of Bayesian statistics Each of the introductory chapters begins by introducing one new concept or assumption Uses "just-in-time mathematics"—the introduction to mathematical ideas just before they are applied
Knowledge In A Nutshell Quantum Physics
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Author : Sten Odenwald
language : en
Publisher: Arcturus Publishing
Release Date : 2020-05-01
Knowledge In A Nutshell Quantum Physics written by Sten Odenwald and has been published by Arcturus Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-01 with Science categories.
Quantum theory is at the heart of modern physics, but how does it actually work? NASA scientist and communicator Sten Odenwald demystifies the subject and makes this crucial topic accessible to everyone. Featuring topics such as Schrodinger's cat, the wave-particle duality and the newly emerging theories of quantum gravity, as well as the personalities behind the science, such as Max Planck, Neils Bohr, Werner Heisenberg, Richard Feynman and many more, Knowledge in a Nutshell: Quantum Physics provides an essential introduction to cutting edge science. Presented in an easy-to-understand format, with diagrams, illustrations and simple summary sections at the end of each chapter, this new addition to the 'Knowledge in a Nutshell' series brings clarity to some of the great mysteries of physics. ABOUT THE SERIES: The 'Knowledge in a Nutshell' series by Arcturus Publishing provides engaging introductions to many fields of knowledge, including philosophy, psychology and physics, and the ways in which human kind has sought to make sense of our world.
Classical Optics And Its Applications
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Author : Masud Mansuripur
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-26
Classical Optics And Its Applications written by Masud Mansuripur and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-26 with Science categories.
Covering a broad range of fundamental topics in classical optics and electro-magnetism, this book is ideal for graduate-level courses in optics, providing supplementary reading materials for teachers and students alike. Industrial scientists and engineers developing modern optical systems will also find it an invaluable resource. Now in color, this second edition contains 13 new chapters, covering optical pulse compression, the Hanbury Brown-Twiss experiment, the Sagnac effect, Doppler shift and stellar aberration, and optics of semiconductor diode lasers. The first half of the book deals primarily with the basic concepts of optics, while the second half describes how these concepts can be used in a variety of technological applications. Each chapter is concerned with a single topic, developing an understanding through the use of diagrams, examples, numerical simulations, and logical arguments. The mathematical content is kept to a minimum to provide the reader with insightful discussions of optical phenomena.
A Concise Introduction To Quantum Mechanics
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Author : Mark S Swanson
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2018-05-10
A Concise Introduction To Quantum Mechanics written by Mark S Swanson and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-10 with Science categories.
Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confi ned to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic fi eld. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
An Introduction To The Uncertainty Principle
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Author : Sundaram Thangavelu
language : en
Publisher:
Release Date : 2003-10-09
An Introduction To The Uncertainty Principle written by Sundaram Thangavelu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with categories.