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The Dirac Equation
Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all aspects cannot be done with sufficient depth within a single volume. In this book the emphasis is on the role of the Dirac equation in the relativistic quantum mechanics of spin-1/2 particles. We cover the range from the description of a single free particle to the external field problem in quantum electrodynamics. Relativistic quantum mechanics is the historical origin of the Dirac equation and has become a fixed part of the education of theoretical physicists. There are some famous textbooks covering this area. Since the appearance of these standard texts many books (both physical and mathematical) on the non relativistic Schrodinger equation have been published, but only very few on the Dirac equation. I wrote this book because I felt that a modern, comprehensive presentation of Dirac's electron theory satisfying some basic requirements of mathematical rigor was still missing.
Visual Quantum Mechanics
"Visual Quantum Mechanics" uses the computer-generated animations found on the accompanying material on Springer Extras to introduce, motivate, and illustrate the concepts explained in the book. While there are other books on the market that use Mathematica or Maple to teach quantum mechanics, this book differs in that the text describes the mathematical and physical ideas of quantum mechanics in the conventional manner. There is no special emphasis on computational physics or requirement that the reader know a symbolic computation package. Despite the presentation of rather advanced topics, the book requires only calculus, making complicated results more comprehensible via visualization. The material on Springer Extras provides easy access to more than 300 digital movies, animated illustrations, and interactive pictures. This book along with its extra online materials forms a complete introductory course on spinless particles in one and two dimensions.
Advanced Visual Quantum Mechanics
Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. Although it is self-contained, this book is part of a two-volume set on Visual Quantum Mechanics. The first book appeared in 2000, and earned the European Academic Software Award in 2001 for oustanding innovation in its field. While topics in book one mainly concerned quantum mechanics in one- and two-dimensions, book two sets out to present three-dimensional systems, the hydrogen atom, particles with spin, and relativistic particles. Together the two volumes constitute a complete course in quantum mechanics that places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor.
Six Stories from the End of Representation
Six Stories is a radically new look at the intersection of science and art through “failed” images.
Imagery in the 21st Century
Scholars from science, art, and humanities explore the meaning of our new image worlds and offer new strategies for visual analysis. We are surrounded by images as never before: on Flickr, Facebook, and YouTube; on thousands of television channels; in digital games and virtual worlds; in media art and science. Without new efforts to visualize complex ideas, structures, and systems, today's information explosion would be unmanageable. The digital image represents endless options for manipulation; images seem capable of changing interactively or even autonomously. This volume offers systematic and interdisciplinary reflections on these new image worlds and new analytical approaches to the visu...
Geometry In Our Three-dimensional World
The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.
Seduced By Mathematics: The Enduring Fascination Of Mathematics
Seduction is not just an end result, but a process — and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people — not just those for whom math plays a key role in their day-to-day lives — have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, 'OMG, that's just amazing,' — because that's what mathematics is to those who love it. In addition, some of the st...
