A First Introduction to Quantum Physics

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In this undergraduate textbook, now in its 2nd edition, the author develops the quantum theory from first principles based on very simple experiments: a photon traveling through beam splitters to detectors, an electron moving through magnetic fields, and an atom emitting radiation. From the physical description of these experiments follows a natural mathematical description in terms of matrices and complex numbers.

The first part of the book examines how experimental facts force us to let go of some deeply held preconceptions and develops this idea into a description of states, probabilities, observables, and time evolution. The quantum mechanical principles are illustrated using applications such as gravitational wave detection, magnetic resonance imaging, atomic clocks, scanning tunneling microscopy, and many more. The first part concludes with an overview of the complete quantum theory.

The second part of the book covers more advanced topics, including the concept of entanglement, the process of decoherence or how quantum systems become classical, quantum computing and quantum communication, and quantum particles moving in space. Here, the book makes contact with more traditional approaches to quantum physics. The remaining chapters delve deeply into the idea of uncertainty relations and explore what the quantum theory says about the nature of reality.

The book is an ideal accessible introduction to quantum physics, tested in the classroom, with modern examples and plenty of end-of-chapter exercises.


Author(s): Pieter Kok
Series: Undergraduate Lecture Notes in Physics
Edition: 2
Publisher: Springer
Year: 2023

Language: English
Pages: 313
City: Cham
Tags: Quantum Physics; Quantum Mechanics; Mach-Zehnder Interferometer; NMR Resonance Imaging; Magnetic Resonance Imaging; Gravitational Wave Detection; Atoms Energy Spectrum; Quantum Information; Quantum Computer; Quantum Teleportation; Uncertainly Relations; Quantum Physics Operational Approach

Preface to the Second Edition
Preface to the First Edition
Contents
List of Figures
1 Three Simple Experiments
1.1 The Purpose of Physical Theories
1.2 Experiment 1: A Laser and A Detector
1.3 Experiment 2: A Laser and A Beam Splitter
1.4 Experiment 3: The Mach–Zehnder Interferometer
1.5 The Breakdown of Classical Concepts
2 Photons and Interference
2.1 The State of a Physical System
2.2 Photon Paths and Superpositions
2.3 Mathematical Intermezzo: Matrix Multiplication
2.4 The Beam Splitter as a Matrix
2.5 Mathematical Intermezzo: Complex Numbers
2.6 The Phase in an Interferometer
2.7 Mathematical Intermezzo: Probabilities
2.8 How to Calculate Probabilities
2.9 Gravitational Wave Detection
2.10 A Quantum Bomb Detector
3 Electrons with Spin
3.1 The Stern-Gerlach Experiment
3.2 The Spin Observable
3.3 The Bloch Sphere
3.4 Uncertainty
3.5 The Magnitude of the Electron Spin
3.6 Photon Polarisation
3.7 39 Magnetic Resonance Imaging
4 Atoms and Energy
4.1 The Energy Spectrum of Atoms
4.2 Changes Over Time
4.3 The Hamiltonian
4.4 Interactions
4.5 Interaction Energy and the Zeeman Effect
4.6 39 The Atomic Clock
5 Operators
5.1 Eigenvalue Problems
5.2 Observables
5.3 Evolution
5.4 The Commutator
5.5 Projectors
6 Entanglement
6.1 The State of Two Electrons
6.2 Entanglement
6.3 Quantum Teleportation
6.4 Mathematical Intermezzo: Qubits and Computation
6.5 39 Quantum Computers
6.6 39 The No-Cloning Theorem and Quantum Cryptography
6.7 39 Entanglement Generation Over Large Distances
7 Decoherence
7.1 Classical and Quantum Uncertainty
7.2 The Density Matrix
7.3 Interactions with the Environment
7.4 Quantum Systems at Finite Temperature
7.5 39 Entropy and Landauer's Principle
7.6 39 Entanglement Measures
8 Motion of Particles
8.1 A Particle in a Box
8.2 Mathematical Intermezzo: The Dirac Delta Function
8.3 The Momentum of a Particle
8.4 Mathematical Intermezzo: Fourier Transforms
8.5 The Energy of a Particle
8.6 39 The Scanning Tunnelling Microscope
8.7 39 A Brief Glance at Chemistry
9 Quantum Uncertainty
9.1 Quantum Uncertainty Revisited
9.2 Uncertainty Relations
9.3 Position-Momentum Uncertainty
9.4 Energy-Time Uncertainty
9.5 The Quantum Mechanical Pendulum
9.6 Schrödinger's Cat
9.7 39 Precision Measurements
10 The History of Quantum Mechanics
11 The Nature of Reality
11.1 The Quantum State Revisited
11.2 Nonlocality
11.3 Contextuality
11.4 A Compendium of Interpretations
11.4.1 The Copenhagen Interpretation
11.4.2 Quantum Bayesianism
11.4.3 Quantum Logic
11.4.4 Objective Collapse Theories
11.4.5 The de Broglie-Bohm Interpretation
11.4.6 Modal Interpretations
11.4.7 The Many Worlds Interpretation
11.4.8 Relational Quantum Mechanics
11.4.9 Other Interpretations
Appendix Epilogue
Appendix Further Reading
Further Reading
Appendix Useful Formulas
Useful Formulas
Appendix Answers to Selected Problems
Answers to Selected Problems
Index