This lively account of the foundations of quantum mechanics is at once elementary and deeply challenging. It is an introduction accessible to anyone with high school mathematics and, at the same time, a rigorous discussion of the most important recent advances in our understanding of quantum physics, a number of them made by the author himself.
This lively account of the foundations of quantum mechanics is at once elementary and deeply challenging. It is an introduction accessible to anyone with high school mathematics and, at the same time, a rigorous discussion of the most important recent advances in our understanding of quantum physics, a number of them made by the author himself.
The more science tells us about the world, the stranger it looks. Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science. This book is an original and provocative investigation of that challenge, as well as a novel attempt at writing about science in a style that is simultaneously elementary and deep. It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some of which are due to the author himself.
Based on years of teaching experience, this book provides a clearly structured and accessible introduction to the fundamental principles of quantum mechanics, tailored for undergraduate students. The text builds a strong conceptual and mathematical foundation while promoting intuitive understanding and critical thinking. Students progress from basic concepts such as wave mechanics to more advanced topics within matrix mechanics. Complex concepts are presented in a diligent and understandable way, achieving a balance between conceptual insight and mathematical rigor without oversimplifying the subject. Thoroughly class-tested, this book is designed to support both classroom instruction and independent study. It will serve as a great tool for undergraduates studying introductory and intermediate quantum mechanics, as well as modern physics and quantum systems for engineers.
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface. The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.
Following the success of The Quantum Universe, first published in 1987, a host of exciting new discoveries have been made in the field of quantum mechanics. The New Quantum Universe provides an up-to-date and accessible introduction to the essential ideas of quantum physics, and demonstrates how it affects our everyday life. Quantum mechanics gives an understanding of not only atoms and nuclei, but also all the elements and even the stars. The book explains quantum paradoxes and the eventful life of Schroedinger's Cat, along with the Einstein–Podolsky–Rosen paradox and Bell's Inequality. It then looks ahead to the nanotechnology revolution, describing quantum cryptography, quantum computing and quantum teleportation, and ends with an account of quantum mechanics and science fiction. Using simple non-mathematical language, this book is suitable for final-year school students, science undergraduates, and anyone wishing to appreciate how physics allows the new technologies that are changing our lives.
An accessible introduction to an exciting new area in computation, explaining such topics as qubits, entanglement, and quantum teleportation for the general reader. Quantum computing is a beautiful fusion of quantum physics and computer science, incorporating some of the most stunning ideas from twentieth-century physics into an entirely new way of thinking about computation. In this book, Chris Bernhardt offers an introduction to quantum computing that is accessible to anyone who is comfortable with high school mathematics. He explains qubits, entanglement, quantum teleportation, quantum algorithms, and other quantum-related topics as clearly as possible for the general reader. Bernhardt, a mathematician himself, simplifies the mathematics as much as he can and provides elementary examples that illustrate both how the math works and what it means. Bernhardt introduces the basic unit of quantum computing, the qubit, and explains how the qubit can be measured; discusses entanglement—which, he says, is easier to describe mathematically than verbally—and what it means when two qubits are entangled (citing Einstein's characterization of what happens when the measurement of one entangled qubit affects the second as “spooky action at a distance”); and introduces quantum cryptography. He recaps standard topics in classical computing—bits, gates, and logic—and describes Edward Fredkin's ingenious billiard ball computer. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. The basic unit of computation is the qubit, not the bit.