Bohmian Mechanics

The Physics and Mathematics of Quantum Theory

AvDetlef Dürr,Stefan Teufel

Inbunden, Engelska, 2009

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2009-05-15
Mått:155 x 235 x undefined mm
Format:Inbunden
Språk:Engelska
Antal sidor:393
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540893431

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Mer om författaren

Detlef Durr studied physics in Munster, Germany, where he obtained his PhD in physics in 1978. After four post-doc years at Rutgers in the group of Joel Lebowitz working with Sheldon Goldstein, he was awarded a Heisenberg fellowship (1985-1989), during which he joined forces with Sheldon Goldstein and Nino Zanghi to develop the statistical analysis of Bohmian mechanics - a cooperation which continues to this day. In 1989 he became professor of mathematics at the University of Munich. His research interests are non-equilibrium statistical mechanics, foundations of statistical mechanics, Bohmian mechanics and the foundations of quantum theory. Stefan Teufel studied physics in Munich, Germany, where he was awarded his PhD in mathematics in 1998. His PhD advisor was Detlef Durr. After one year as a post doc at Rutgers with Sheldon Goldstein he joined the group of Herbert Spohn at the Technical University of Munich. In 2004 he became lecturer in mathematics at Warwick University, UK. Since 2005 he has been full professor of mathematics at the University of Tubingen. His research interests include adiabatic and semiclassical problems in quantum dynamics, exponential asymptotics and Bohmian mechanics.

Recensioner i media

From the reviews: "In this extremely important and well-written book is that there is indeed a genuine problem with ordinary quantum mechanics, but also that there is a solution. ... It offers a detailed, pedagogical, and comprehensive discussion of a solution to the conceptual problems of quantum mechanics: Bohmian mechanics. ... This book contains a lot more than the best existing exposition of Bohm's theory. ... it also contains a lot of good philosophical observations." (Jean Bricmont, Metascience, Vol. 20 (1), March, 2011) "This book is both an introduction to and a case for Bohmian quantum mechanics. It attempts to expose the myths surrounding the approach and to clarify its formal and physical basis. ... It is certainly the best book on the Bohmian approach currently on the market ... ." (Dean Rickles, Mathematical Reviews, Issue 2011 h)

Innehållsförteckning

Classical Physics.- Symmetry.- Chance.- Brownian motion.- The Beginning of Quantum Theory.- Schr#x00F6;dinger#x2019;s Equation.- Bohmian Mechanics.- The Macroscopic World.- Nonlocality.- The Wave Function and Quantum Equilibrium.- From Physics to Mathematics.- Hilbert Space.- The Schr#x00F6;dinger Operator.- Measures and Operators.- Bohmian Mechanics on Scattering Theory.- Epilogue.