Bohmian Mechanics as the Foundation of Quantum Mechanics

1. Auflage 2009
ISBN: 978-1-4020-9429-3
Verlag: Springer Netherlands

Buch, Englisch, Band 1005, 391 Seiten, GB, Format (B × H): 155 mm x 235 mm

Reihe: Fundamental Theories of Physics

Bohmian Mechanics was found 1952 by David Bohm as an ontological theory of quantum phenomena. It had been revived in the second half of the last century 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 ist 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, it develops carefully the insight for the need of the mathematics of quantum mechanics, which is carried out with full mathematical rigor.

Autoren/Hrsg.

Teufel, Stefan

Dürr, Detlef

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Quantenphysik Atom- und Molekülphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Introduction.- Classical Physics.- Symmetry.- Chance.- Brownian motion.- The Beginning of Quantum Theory.- Schrödinger’s Equation.- Bohmian Mechanics.- The MacroscopicWorld.- Nonlocality.- The Wave Function and Quantum Equilibrium.- From Physics to Mathematics.- Hilbert Space.- The Schrödinger Operator.- Measures and Operators.- Bohmian Mechanics on Scattering Theory.- Epilogue.

Über Autor(innen)

Detlef Durr: 1978 PhD in physics, Department of Physics University of Muenster 1979-1984 post Doc Department of Mathematics, Rutgers University 1984-1989 Heisenberg fellow (DFG stipend) after Habilitation in Bochum Since 1989 Professor at the Department of Mathematics, LMU Munchen Author of: Bohmsche Mechanik als Grundlage der Quantenmechanik, Guesteditor of the IOP volume: The quantum universe Editor of Springer Lecture Notes in Physics: Chance in Physics: Foundations and Perspectives Stefan Teufel: 1998 PhD in mathematics, Mathematics Department, LMU Munich 1999-2003 Assistant at the Center for Mathematics, TU Munich 2004 Lecturer at the Mathematics Department of Warwick University, UK Since 2005 Professor at the Mathematics Institute, University of Tubingen Author of: Adiabatic perturbation theory in quantum dynamics Lecture Notes in Mathematics 1821. Springer-Verlag, Berlin, Heidelberg, New York, 2003.