Bernd Thaller – författare

Advanced 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. It also contains a basic course on quantum information theory, introducing topics like quantum teleportation, the EPR paradox, and quantum computers. 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. The reader is expected to be familiar with calculus and elementary linear algebra. Any further mathematical concepts will be illustrated in the text. The CD-ROM includes a large number of Quick-Time movies presented in a multimedia-like environment.The movies illustrate and add color to the text, and allow the reader to view time-dependent examples with a level of interactivity. The point-and-click interface is no more difficult than using the internet. This book has a home page (http://vqm.uni-graz.at) that includes more supplementary material, additional animations and visualizations, Mathematica notebooks, and further information."

In the strange world of quantum mechanics the application of visualization techniques is particularly rewarding, for it allows us to depict phenomena that cannot be seen by any other means. Visual Quantum Mechanics relies heavily on visualization as a tool for mediating knowledge. The book comes TM with a CD-ROM containing about 320 digital movies in QuickTime f- mat, which can be watched on every multimedia-capable computer. These computer-generated animations are used to introduce, motivate, and ill- trate the concepts of quantum mechanics that are explained in the book. If a picture is worth a thousand words, then my hope is that each short animation (consisting of about a hundred frames) will be worth a hundred thousand words. The collection of ?lms on the CD-ROM is presented in an interactive en- TM vironmentthathasbeendevelopedwiththehelpofMacromediaDirector . This multimedia presentation can be used like an adventure game without special computer skills. I hope that this presentation format will attract the interest of a wider audience to the beautiful theory of quantum mechanics.

Visual Quantum Mechanics

100 ways to get students hooked on math!It happens to the best of us: that one question that’s got you stumped. Or maybe you have the answer, but it’s not all that compelling or convincing. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students’ 100 most frequently asked math questions. Even if you already have the answers, Al’s explanations are certain to keep kids hooked—and that’s what it’s all about.The questions are all organized around the Common Core’s math content standards and relate directly to Numbers and Quantity, Functions, Algebra, Geometry, and Statistics and Probability. The big benefits? You’ll discover high-interest ways to:• Teach inquiry and process in mathematical thinking• Encourage flexibility in problem solving• Emphasize efficient test-taking strategies • Provide practical applications from mathematics, education, and human development research• Build students’ procedural skills and conceptual understanding Use this complete resource to save time, anticipate questions, promote process and thinking, and present yourself as the math expert we know you are.

In the strange world of quantum mechanics the application of visualization techniques is particularly rewarding, for it allows us to depict phenomena that cannot be seen by any other means. I hope that this presentation format will attract the interest of a wider audience to the beautiful theory of quantum mechanics.

Did you grow up thinking math is boring? It's time to reconsider. This book will teach you everything you ever wondered about numbers-and more.How and why did human beings first start using numbers at the dawn of history? Would numbers exist if we Homo sapiens weren't around to discover them? What's so special about weird numbers like pi and the Fibonacci sequence? What about rational, irrational, real, and imaginary numbers? Why do we need them?Two veteran math educators explain it all in ways even the most math phobic will find appealing and understandable.You'll never look at those squiggles on your calculator the same again.

"The Dirac Equation" is a modern presentation of the realistic quantum mechanics of electrons intended to make new mathematical results accessible to a wider audience. It treats in some depth the relativistic invariance of a quantum theory, self-adjointness and spectral theory, qualitative features of relativistic bound and scattering states, and the external field problem in quantum electrodynamics, without neglecting the interpretational difficulties and limitations of the theory. A novel feature is the extensive use of supersymmetric quantum mechanics in the discussions of, e.g. the nonrelativistic limit, Fredholm and Witten indices, the relativistic Coulomb problem, particles with anomalous moments, behaviour in the presence of magnetic fields, and soliton theory. The book is aimed at scientists and graduate students interested in quantum mechanics who want to learn about the mathematical foundations, the physical interpretation and important applications of Dirac's electron theory.

The Dirac Equation is a modern presentation of the relativistic quantum mechanics of electrons intended to make new mathematical results accessible to a wider audience. It treats in some depth the relativistic invariance of a quantum theory, self-adjointness and spectral theory, qualitative features of relativistic bound and scattering states, and the external field problem in quantum electrodynamics, without neglecting the interpretational difficulties and limitations of the theory. A novel feature is the extensive use of supersymmetric quantum mechanics in the discussions of, e.g. the nonrelativistic limit, Fredholm and Witten indices, the relativistic Coulomb problem, particles with anomalous moments, behaviour in the presence of magnetic fields, and soliton theory. The book is aimed at scientists and graduate students interested in quantum mechanics who want to learn about the mathematical foundations, the physical interpretation and important applications of Dirac's electron theory.

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.

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.