An Introduction To The Uncertainty Principle

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681647

Get Book

An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

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.

Author : Sundaram Thangavelu
Publisher : Unknown
Page : 174 pages
File Size : 51,6 Mb
Release : 2004
Category : Harmonic analysis
ISBN : LCCN:03050228

Get Book

An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

Author : Victor Havin,Burglind Jöricke
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642783777

Get Book

The Uncertainty Principle in Harmonic Analysis by Victor Havin,Burglind Jöricke Pdf

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).

Author : Joseph B. Kadane
Publisher : CRC Press
Page : 525 pages
File Size : 50,6 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781351683364

Get Book

Principles of Uncertainty by Joseph B. Kadane Pdf

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

Author : Werner Heisenberg
Publisher : Courier Corporation
Page : 208 pages
File Size : 45,6 Mb
Release : 2013-04-15
Category : Science
ISBN : 9780486318417

Get Book

The Physical Principles of the Quantum Theory by Werner Heisenberg Pdf

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.

Author : OpenStax
Publisher : Unknown
Page : 622 pages
File Size : 48,7 Mb
Release : 2016-11-04
Category : Science
ISBN : 1680920456

Get Book

University Physics by OpenStax Pdf

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.

Author : William C. Price,Seymour S. Chissick
Publisher : John Wiley & Sons
Page : 586 pages
File Size : 43,6 Mb
Release : 1977
Category : Science
ISBN : MINN:31951000562738F

Get Book

The Uncertainty Principle and Foundations of Quantum Mechanics by William C. Price,Seymour S. Chissick Pdf

Author : Linus Pauling,E. Bright Wilson
Publisher : Courier Corporation
Page : 496 pages
File Size : 52,6 Mb
Release : 2012-06-08
Category : Science
ISBN : 9780486134932

Get Book

Introduction to Quantum Mechanics with Applications to Chemistry by Linus Pauling,E. Bright Wilson Pdf

Classic undergraduate text explores wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, and the structure of simple and complex molecules. Numerous tables and figures.

Author : David Lindley
Publisher : Anchor
Page : 274 pages
File Size : 55,5 Mb
Release : 2008-02-12
Category : Science
ISBN : 9780307389480

Get Book

Uncertainty by David Lindley Pdf

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.

Author : IntroBooks Team
Publisher : IntroBooks
Page : 128 pages
File Size : 46,8 Mb
Release : 2024-06-18
Category : Science
ISBN : 8210379456XXX

Get Book

Uncertainty Principle of Werner Heisenberg by IntroBooks Team Pdf

Quantum mechanics is widely considered to be the scientific theory that is one's best choice for the fundamental and universal explanation of the physical world. The conceptual structure used in this theory varies dramatically from that of classical physics. After all, the transition from classical to quantum physics is a true revolution in people's understanding of the physical universe. One striking feature of the distinction between classical and quantum physics is that while classical mechanics assumes that precise simultaneous values can be assigned to all physical quantities, quantum mechanics, on the other hand, rejects this possibility, the classic example being the momentum and position of a particle.

Author : Robert P Crease
Publisher : National Geographic Books
Page : 0 pages
File Size : 50,8 Mb
Release : 2015-12-01
Category : Science
ISBN : 9780393351927

Get Book

The Quantum Moment by Robert P Crease Pdf

"A very fun way to learn about where quantum physics comes from and the strange, even astonishing places it has gone." —Peter Galison, Harvard University, author of Einstein’s Clocks, Poincaré’s Maps From multiverses and quantum leaps to Schrödinger’s cat and time travel, quantum mechanics has irreversibly shaped the popular imagination. Entertainers and writers from Lady Gaga to David Foster Wallace take advantage of its associations and nuances. In The Quantum Moment, philosopher Robert P. Crease and physicist Alfred Scharff Goldhaber recount the fascinating story of how the quantum jumped from physics into popular culture, with brief explorations of the underlying math and physics concepts and descriptions of the fiery disputes among figures including Einstein, Schrödinger, and Niels Bohr. Understanding and appreciating quantum imagery, its uses and abuses, is part of what it means to be an educated person in the twenty-first century. The Quantum Moment serves as an indispensable guide.

Author : John Polkinghorne
Publisher : OUP Oxford
Page : 145 pages
File Size : 47,9 Mb
Release : 2002-05-30
Category : Science
ISBN : 9780191577673

Get Book

Quantum Theory: A Very Short Introduction by John Polkinghorne Pdf

Quantum Theory is the most revolutionary discovery in physics since Newton. This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Author : Mark S Swanson
Publisher : Morgan & Claypool Publishers
Page : 185 pages
File Size : 52,7 Mb
Release : 2018-05-10
Category : Science
ISBN : 9781681747163

Get Book

A Concise Introduction to Quantum Mechanics by Mark S Swanson Pdf

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.

Author : Masud Mansuripur
Publisher : Cambridge University Press
Page : 0 pages
File Size : 47,7 Mb
Release : 2009-02-26
Category : Science
ISBN : 9780521881692

Get Book

Classical Optics and Its Applications by Masud Mansuripur Pdf

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.

Author : Werner Heisenberg
Publisher : Courier Corporation
Page : 212 pages
File Size : 46,5 Mb
Release : 1949-01-01
Category : Science
ISBN : 0486601137

Get Book

The Physical Principles of the Quantum Theory by Werner Heisenberg Pdf

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.