Quantum Mechanics: A Concise Introduction

Description

This textbook highlights a concise introduction to quantum mechanics in a readable and serious manner. Being readable, the book intends to present the beauty and magic of quantum mechanics to the mass public. Being serious, the book uses mathematics to describe the most profound results in quantum mechanics. To balance the two, the book assumes that the readers are familiar with high-school mathematics and instructs the least possible advanced mathematics necessary for the understanding of quantum mechanics. The book first covers the history of quantum mechanics and then introduces the magical quantum world, including quantum states living in Hilbert space, indistinguishable particles, linear superposition, Heisenberg's uncertainty relations, quantum entanglement, Bell's inequality, quantum energy levels, Schrödinger’s cat and many-worlds theory, etc. To compare with classic physics, the book also covers the classic mechanics before introducing quantum mechanics. At last, the book briefly covers quantum computing and quantum communications.  Besides readers of other majors, the book is also a good reference for students in physics. It helps physics students to develop a solid understanding of the basics of quantum mechanics, preventing them from getting lost in solving the Schrödinger equation. The book also discusses quantum entanglement and quantum information which traditional quantum mechanics textbooks do not cover.  The Foreword is written by Frank Wilczek, Nobel Laureate in physics, 2004. This book is a translation of an original Chinese edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.  Foreword Translator’s Preface Preface Acknowledgements Contents 1 What Is Quantum? 2 A Brief History of Quantum Mechanics 2.1 The Birth of Quantum 2.2 The Difficult Start 2.3 Hydrogen Atom 2.4 The Crisis 2.5 Identical Particles 2.6 It's Matrix 2.7 Particles Are Waves and Waves Are Particles 2.8 Retrospect 3 Classical Mechanics and the Old Quantum Theory 3.1 Free Fall 3.2 Phase Space 3.3 Calculus for Velocity and Acceleration 3.4 Harmonic Oscillator 3.5 The Old Quantum Theory 4 Complex Number and Linear Algebra 4.1 Complex Number 4.2 Linear Algebra 4.2.1 Linear Space 4.2.2 Hilbert Space 4.2.3 Matrix 4.2.4 Eigenstates and Eigenvalues 4.2.5 Direct Product 5 Into the Quantum World 5.1 The Stern-Gerlach Experiment 5.2 Spin 5.3 Quantum State and Its Statistical Interpretation 5.4 Observables and Operators 5.5 Spin Along an Arbitrary Direction 5.6 Theoretical Framework of Quantum Mechanics 6 Quantum Dynamics 6.1 Schrödinger Equation 6.2 Wave Function 6.3 Hamiltonian Operator and Unitary Evolution 6.4 Quantum Energy Levels and Eigenstates 6.5 Superposition Principle of Quantum States and No-cloning Theorem 6.6 Double-Slit Interference 7 Quantum Entanglement and Bell's Inequality 7.1 System of Two Spins 7.2 Quantum Entanglement 7.2.1 Bell's Inequality 7.2.2 Loss of Individuality 8 Quantum Measurement 8.1 The Uncertainty Relation 8.2 Collapse of a Wave Function 8.3 Many-Worlds Theory and Schrödinger's Cat 8.4 Flaws in Feynman's Argument 9 Quantum Computation 9.1 Classical Computer 9.1.1 Basic Framework 9.1.2 The Unbearable Quantum 9.2 Quantum Computer 9.3 Reversible Classical Computers 9.4 How Powerful Is a Quantum Computer 9.5 Technical Difficulties of Building a Quantum Computer 10 Quantum Communication 10.1 Polarization of Photons 10.2 Quantum Teleportation 10.3 Classic Encryption 10.4 Quantum Key Distribution 10.5 Future Quantum Technologies Appendix Further Reading Index