This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

This book is about the epistemology of quantum physics and its interpretation as a scientific theory in its technical form. The contents of the book are essentially of non-formal nature although the formalism of quantum mechanics is also investigated (rather briefly) inline with the needs and requirements of the epistemological investigation and considerations. The reader should note that a general scientific and mathematical background (at the undergraduate level) is required to understand the book properly and appreciate its contents. The book is like my previous books in style and favorable characteristics (such as clarity, graduality and intensive cross referencing with hyperlinks in the electronic versions). However, the book, unlike my previous books, does not contain questions or exercises or solved problems. The book is particularly useful to those who have special interest in the interpretative aspects of quantum theory and the philosophy of science although it should be useful even to those who are interested in the purely-scientific and technical aspects of the quantum theory since the contents of the book should broaden the understanding of these aspects and provide them with qualitative and interpretative dimensions (as well as the added benefit of the brief investigation of the formalism of quantum mechanics).

The author does not want a book description on the back cover.

The Physics of Theism provides a timely, critical analysis of the ways in which physics intertwines with religion. Koperski brings clarity to a range of arguments including the fine-tuning argument, naturalism, the laws of nature, and the controversy over Intelligent Design. A single author text providing unprecedented scope and depth of analysis of key issues within the Philosophy of Religion and the Philosophy of Science Critically analyses the ways in which physics is brought into play in matters of religion Self-contained chapters allow readers to directly access specific areas of interest The area is one of considerable interest, and this book is a timely and well-conceived contribution to these debates Written by an accomplished scholar working in the philosophy of physics in a style that renders complex arguments accessible

In this book Drs J X Zheng-Johansson and Per-Ivar Johansson present a remarkable unification scheme. The scheme is based on an analysis of the overall experimental observations available up to today, and an observation of the unsolved problems maintained in contemporary theoretical physics, revisiting past controversies and putting them in context with contemporary physics. The unsolved problems were the agent stimulating the authors to invent a new bold unification scheme. Vacuum polarisation, with a vacuuon (a pair of strongly bound opposite-signed charges) as a free entity, gets you back to the days of the ether concept, abandoned by physics after the Michelson-Morley experiment by the end of the 19:th century. Starting from constructing the fundamental building blocks for the vacuum and material particles, the Newtonian-Maxwellian solutions the authors obtain yield insights into fundamental concepts such as vacuum, charge, and mass. For instance, can vacuum be described by a building block denoted vacuuon, with or without mass depending on pushed into motion or not? Can free charges be described as a mass-less entity? Can and how vacuum polarise? However, even if vacuum in the real Universe never polarises as proposed in this unification scheme, it may yet serve as another tool in the physics toolbox, a theoretical bridge between classical and modern physics. Physics and physical theory is a human invention, a mathematical description of the intrinsic properties of the Universe and its associated phenomena. Our understanding of the Universe is a reaction of our mind, of our way of understanding. Richard Feynman once noted about the Maxwell equations something that goes like: If a mathematical theory in physics cannot be proved by experiments it remains to be proved mathematically. Ultimately, it must be possible to test any new theory by experiments. If experimental tests are not possible we are left with a mere hypothesis based on equations. The unification scheme proposed by this work consists of a Proposition about the fundamental building blocks (ap- and n-vaculeon) and a series of Predictions from Newtonian-Maxwellian solutions based on that Proposition. The arriving at the Proposition and the Predictions, relating to classical, quantum and relativistic mechanics, is their context. The book is a challenge out of the ordinary, a challenge that deserves careful consideration.

Quantum theory as a scientific revolution profoundly influenced human thought about the universe and governed forces of nature. Perhaps the historical development of quantum mechanics mimics the history of human scientific struggles from their beginning. This book, which brought together an international community of invited authors, represents a rich account of foundation, scientific history of quantum mechanics, relativistic quantum mechanics and field theory, and different methods to solve the Schrodinger equation. We wish for this collected volume to become an important reference for students and researchers.

John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics. The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.

The book explores several open questions in the philosophy and the foundations of statistical mechanics. Each chapter is written by a leading expert in philosophy of physics and/or mathematical physics. Here is a list of questions that are addressed in the book: