Stefan Teufel - Böcker

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics.

Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit.A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.

Bohmian Mechanics was formulated in 1952 by David Bohm as an ontological theory of quantum phenomena. It was revived some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. The theory is about the motion of point particles, the statistical analysis of which, yields the formalism of quantum mechanics in terms of Hilbert spaces, self-adjoint operator-observables, and projection and positive operator valued measures. Tunneling times, arrival times, and first exit times are easily described within Bohmian mechanics. The book explains how Boltzmann 's probabilistic reasoning in statistical mechanics when applied to Bohmian mechanics leads to a rational account of quantum mechanics and its mathematical abstractions. It provides the insight and the mathematical tools to establish the formalism of quantum theory, including scattering theory, as the statistical macroscopic description of Bohmian mechanics.It reviews the essentials of classical physical theories relevant to the probabilistic reasoning and introduces Bohmian mechanics from various points of views.It provides rational perspectives on identical particles (bosons and fermions), the classical limit, quantum equilibrium , uncertainty relation and quantum observables. The book is self-contained, mathematically rigorous and the best possible starting point for a full understanding of quantum mechanics according to Bohm and Bell. It will appeal to students and newcomers, as well as to established scientists seeking a clear exposition of the theory.