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 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).

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.

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.

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 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.

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.