Foundations of quantum mechanics / Roderich Tumulka.

Format:

Book

Author/Creator:

Tumulka, Roderich, author.

Series:

Lecture notes in physics ; 1003.

Lecture notes in physics, 1616-6361 ; volume 1003

Language:

English

Subjects (All):

Quantum theory.

Genre:

Electronic books.

Physical Description:

1 online resource (xvii, 468 pages) : illustrations.

Place of Publication:

Cham, Switzerland : Springer, 2022.

Summary:

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 Bells 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.

Contents:

Intro

Preface

Contents

Acronyms

1 Waves and Particles

1.1 Overview

1.2 The Schrödinger Equation

1.3 Unitary Operators in Hilbert Space

1.3.1 Existence and Uniqueness of Solutions of the Schrödinger 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 Properties of Bohmian Mechanics

1.6.3 Historical Overview

1.6.4 Equivariance

1.6.5 The Double-Slit Experiment in Bohmian Mechanics

1.6.6 Delayed-Choice Experiments

Afshar's Experiment

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

2.1.5 External Magnetic Field

2.2 Operators and Observables

2.2.1 Heisenberg's Uncertainty Relation

2.2.2 Limitation to Knowledge

2.2.3 Self-Adjoint Operators

2.2.4 The Spectral Theorem

2.2.5 Born's Rule

2.2.6 Conservation Laws in Quantum Mechanics

2.2.7 The Dirac Delta Function

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 Are There Actual Spin Values?

2.3.7 Many-Particle Systems

2.3.8 Representations of SO(3)

2.3.9 Inverted Stern-Gerlach Magnet and Contextuality

Exercises

3.3.4 Primitive Ontology

3.3.5 How GRW Theory Solves the Measurement Problem

3.3.6 Empirical Tests

3.3.7 The Need for a Primitive Ontology

3.4 The Copenhagen Interpretation

3.4.1 Two Realms

3.4.2 Elements of the Copenhagen View

Positivism

Purported Impossibility of Non-paradoxical Theories

Completeness of the Wave Function

Language of Measurement

Narratives, But No Serious Ones

3.4.3 Complementarity

3.4.4 Reactions to the Measurement Problem

3.4.5 The Transactional Interpretation

3.5 Many Worlds

3.5.1 Schrödinger's Many-Worlds Theory

Notes:

Includes bibliographical references and indexes.

Print version record.

Other Format:

Print version: TUMULKA, RODERICH. FOUNDATIONS OF QUANTUM MECHANICS.

ISBN:

9783031095481

3031095480

OCLC:

1352092403

Access Restriction:

Restricted for use by site license.