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An Introduction To The Uncertainty Principle

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Author by : Sundaram Thangavelu
Languange Used : en
Release Date : 2012-12-06
Publisher by : Springer Science & Business Media

ISBN : 9780817681647

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....

An Introduction To The Uncertainty Principle

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Author by : Sundaram Thangavelu
Languange Used : en
Release Date : 2004
Publisher by :

ISBN : LCCN:03050228

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The Physical Principles Of The Quantum Theory

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Author by : Werner Heisenberg
Languange Used : en
Release Date : 2013-04-15
Publisher by : Courier Corporation

ISBN : 9780486318417

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....

Principles Of Uncertainty

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Author by : Joseph B. Kadane
Languange Used : en
Release Date : 2020-11-25
Publisher by : CRC Press

ISBN : 9781351683364

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...

The Uncertainty Principle

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Author by : Robyn Williams
Languange Used : en
Release Date : 1991-01
Publisher by :

ISBN : 0733301258

A new, enlarged edition of collected conversations with leading scientists, originally shown on the ABC television series of the same name. The new edition includes interviews from the second television series, including encounters with Sir Mark Oliphant, Sir Gustav Nossal, John Dawkins and Harry Butler. The first edition was published in 1989. Williams is now chairman of the Commission for the Future....

The Uncertainty Principle In Harmonic Analysis

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Author by : Victor Havin
Languange Used : en
Release Date : 2012-12-06
Publisher by : Springer Science & Business Media

ISBN : 9783642783777

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)....

Uncertainty

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Author by : David Lindley
Languange Used : en
Release Date : 2008-02-12
Publisher by : Anchor

ISBN : 9780307389480

The gripping, entertaining, and vividly-told narrative of a radical discovery that sent shockwaves through the scientific community and forever changed the way we understand the world. Werner Heisenberg’s “uncertainty principle” challenged centuries of scientific understanding, placed him in direct opposition to Albert Einstein, and put Niels Bohr in the middle of one of the most heated debates in scientific history. Heisenberg’s theorem stated that there were physical limits to what we could know about sub-atomic particles; this “uncertainty” would have shocking implications. In a riveting and lively account, David Lindley captures this critical episode and explains one of the most important scientific discoveries in history, which has since transcended the boundaries of science and influenced everything from literary theory to television....

University Physics

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Author by : OpenStax
Languange Used : en
Release Date : 2016-11-04
Publisher by :

ISBN : 1680920456

University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale....

The Uncertainty Principle

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Author by : Marty L. Williams
Languange Used : en
Release Date : 1998
Publisher by :

ISBN : OCLC:40828141

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Uncertainty Principle 164 Success Secrets 164 Most Asked Questions On Uncertainty Principle What You Need To Know

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Author by : Theresa Hardy
Languange Used : en
Release Date : 2014-10-06
Publisher by : Emereo Publishing

ISBN : 148885193X

The latest and the greatest Uncertainty principle. There has never been a Uncertainty principle Guide like this. It contains 164 answers, much more than you can imagine; comprehensive answers and extensive details and references, with insights that have never before been offered in print. Get the information you need--fast! This all-embracing guide offers a thorough view of key knowledge and detailed insight. This Guide introduces what you want to know about Uncertainty principle. A quick look inside of some of the subjects covered: Quantum entanglement - Concept, Planck scale, Quantum effects, Complementarity (physics), Introduction to quantum mechanics, Point mass - In quantum mechanics, Copenhagen Interpretation - Principles, Superresolution - Basic Concepts, Determinism -, Howard P. Robertson, Pauli exclusion principle - Stability of matter, Short-time Fourier transform - Resolution issues, Basic concepts of quantum mechanics, Heisenberg's microscope, Popper's experiment - Realization of Popper's experiment, Double-slit experiment - Weak measurement, Introduction to quantum mechanics - Uncertainty principle, Angular momentum operator - Uncertainty principle, Quantum mechanics - Free particle, Anomaly in software - Debugging, Atomic theory - Quantum physical models of the atom, Preon - The mass paradox, Quantum cognition - Additional Reading, Virtual particles, Delayed choice quantum eraser - Introduction, QED vacuum - Virtual particles, Classical information - Classical versus quantum information, Arthur Stanley Eddington - Idealism, Elementary particles - String theory, Cosmic inflation - Inflation and generalized uncertainty principle (GUP), Virtual particle - Properties, Arthur Eddington - Idealism, Uncertainty principle - Introduction, Annihilation - Electron-positron annihilation, Quantum effects - Mathematical formulations, and much more......