Foundations of Quantum Mechanics - Paperback

by Roderich Tumulka (Author)

Preface

1. Waves and Particles

1.1 Overview

1.2 The Schrodinger Equation

1.3 Unitary Operators in Hilbert Space

1.3.1 Existence and Uniqueness of Solutions of the Schrodinger Equation

1.3.2 The Time Evolution Operators

1.3.3 Unitary Matrices and Rotations

1.3.4 Inner Product

1.3.5 Abstract Hilbert Space

1.4 Classical Mechanics

1.4.1 Definition of Newtonian Mechanics

1.4.2 Properties of Newtonian Mechanics

1.4.3 Hamiltonian Systems

1.5 The Double Slit Experiment

1.5.1 Classical Predictions for Particles and Waves

1.5.2 Actual Outcome of the Experiment

1.5.3 Feynman's Discussion

1.6 Bohmian Mechanics

1.6.1 Definition of Bohmian Mechanics

1.6.2 Historical Overview

1.6.3 Equivariance

1.6.4 The Double Slit Experiment in Bohmian Mechanics

1.6.5 Delayed Choice Experiments

Summary

Exercises

References

2. Some Observables

2.1 Fourier Transform and Momentum

2.1.1 Fourier Transform

2.1.2 Momentum

2.1.3 Momentum Operator

2.1.4 Tunnel Effect

2.2 Operators and Observables

2.2.1 Heisenberg's Uncertainty Relation

2.2.2 Self-Adjoint Operators

2.2.3 The Spectral Theorem

2.2.4 Conservation Laws in Quantum Mechanics

2.3 Spin

2.3.1 Spinors and Pauli Matrices

2.3.2 The Pauli Equation

2.3.3 The Stern-Gerlach Experiment

2.3.4 Bohmian Mechanics with Spin

2.3.5 Is an Electron a Spinning Ball?

2.3.6 Is There an Actual Spin Vector?

2.3.7 Many-Particle Systems

2.3.8 Representations of SO(3)

2.3.9 Inverted Stern-Gerlach Magnet and Contextuality

Summary

Exercises

References

3. Collapse and Measurement

3.1 The Projection Postulate

3.1.1 Notation

3.1.2 The Projection Postulate

3.1.3 Projection and Eigenspace

3.1.4 Remarks

3.2 The Measurement Problem

3.2.1 What the Problem Is

3.2.2 How Bohmian Mechanics Solves the Measurement P

Back Jacket

This book introduces and critically appraises the main proposals for how to understand quantum mechanics, namely the Copenhagen interpretation, spontaneous collapse, Bohmian mechanics, many-worlds, and others. The author makes clear what are the crucial problems, such as the measurement problem, related to the foundations of quantum mechanics and explains the key arguments like the Einstein-Podolsky-Rosen argument and Bell's proof of nonlocality. He discusses and clarifies numerous topics that have puzzled the founding fathers of quantum mechanics and present-day students alike, such as the possibility of hidden variables, the collapse of the wave function, time-of-arrival measurements, explanations of the symmetrization postulate for identical particles, or the nature of spin. Several chapters are devoted to extending the different approaches to relativistic space-time and quantum field theory. The book is self-contained and is intended for graduate students and researchers who want to step into the fundamental aspects of quantum physics. Given its clarity, it is accessible also to advanced undergraduates and contains many exercises and examples to master the subject.

Author Biography

Roderich Tumulka earned a Ph.D. in mathematics from Ludwig Maximilians University in Munich. During the period 2007-2016, he taught at Rutgers University (USA) and has since taught at Eberhard Karls University in Tübingen (Germany). His field of research is mathematical physics, focusing particularly on the foundations of quantum mechanics, quantum field theory, and quantum statistical mechanics.