Quantum Mechanics: The Theoretical Minimum

Citation

Susskind, L., & Friedman, A. (2015). Quantum Mechanics: The Theoretical Minimum. Basic Books.

Chapter Summary

The book has ten chapters, which the publisher says run parallel to Susskind's Stanford continuing-education course on quantum mechanics, and each chapter includes exercises. It is the second volume of the Theoretical Minimum series, following a volume on classical mechanics. Chapter titles come from a library catalogue record; the descriptions of what the chapters do rely on the publisher's description, a Publishers Weekly review and a review by C. Burrell, and are given in groups because the sources do not describe each chapter separately.

Chapters 1–3: Systems and Experiments; Quantum States; Principles of Quantum Mechanics

According to Burrell, the authors begin with a simple quantum system, a single quantum spin, and use it to lay out the unusual logic of quantum states and how it differs from classical logic. These chapters establish the framework (states, and the principles that govern them) on which everything else is built. Publishers Weekly notes that the text presents spin and qubits, and that much of it is mathematics, from Boolean logic and statistics to vectors and matrices.

Chapters 4–5: Time and Change; Uncertainty and Time Dependence

Burrell says the authors discuss both time-independent and time-dependent quantum mechanics, stressing the former for finding the energy states of a system and the latter for finding how it evolves in time. Time evolution and the Heisenberg uncertainty principle, both mentioned by Publishers Weekly, belong to this part of the book.

Chapters 6–7: Combining Systems: Entanglement; More on Entanglement

Entanglement receives two chapters, and Burrell estimates that about one-third of the book is devoted to it. He adds that the authors argue that entanglement does not imply any sort of non-locality, contrary to what is sometimes claimed.

Chapters 8–9: Particles and Waves; Particle Dynamics

Burrell describes the later sections as a transition to wavefunctions and particles that creeps up to the edge of quantum field theory so as to peer over it. Publishers Weekly lists wave functions and the Schrödinger equation among the concepts presented.

Chapter 10: The Harmonic Oscillator

The book ends with the quantum harmonic oscillator, which Burrell calls one of the simplest but most important quantum systems.

Key Concepts

Chapters 1–5: States, principles and time evolution

• Quantum spin and qubits: the simple system with which the book starts.
• Quantum states: the subject of Chapter 2.
• Uncertainty principle: the topic of Chapter 5.

Chapters 6–10: Entanglement, waves and the oscillator

• Entanglement: the subject of Chapters 6 and 7.
• Wavefunctions and the Schrödinger equation: the particle and wave chapters.
• Harmonic oscillator: Chapter 10.

Critical Analysis

Strengths

• Conceptual and mathematical together. Burrell observes that the book is neither a popular introduction nor an advanced text: it explores the conceptual foundations carefully and also has enough gentle, pertinent mathematics for the reader to see how famous predictions follow.
• Clear teaching. He notes that intermediate steps are worked, the significance of conclusions is emphasised and the tone is welcoming, with the mathematics (complex numbers, basic calculus, linear algebra) given quick explanations in the text.
• Exercises in each chapter. The publisher stresses exercises to ensure mastery of each area, and the book is built to be worked through rather than only read.
• A distinctive route. Starting from spin and the logic of states rather than from wave mechanics lets entanglement and measurement be treated early and at length.

Limitations

• Mathematics dominates. Publishers Weekly describes the book as an introduction to the advanced mathematics needed for the subject, and notes that most of the text focuses on mathematics, so it is not an easy popular read.
• Unclear target audience. Burrell finds it hard to say who the book is for; he suggests it could suit an engineering-trained reader, an ambitious high-school student or a returning physicist.
• Not a full course. The ten chapters end at the harmonic oscillator, and the titles list no chapters on approximation methods or scattering, so a university course will need a textbook.

Where It Fits in the Course

Susskind and Friedman is the self-study entry on the quantum mechanics list. Rae and Napolitano's Quantum Mechanics is a compact textbook for a first university course, developing wave mechanics from experimental evidence before angular momentum, approximation methods and many-particle systems. Griffiths's Introduction to Quantum Mechanics is a university textbook, and Sakurai and Napolitano's Modern Quantum Mechanics is a mathematically mature text that uses Dirac notation and goes through angular momentum, symmetries, approximation methods and scattering.

Albert's Quantum Mechanics and Experience is a conceptual guide to states, measurement, nonlocality and interpretation without a full formal apparatus. Read before a university course, Susskind and Friedman builds the state-based viewpoint on which a text such as Sakurai's rests; read alongside it, it supplies a gentler second explanation.

How to Use This Book

The page metadata lists basic algebra and calculus, with complex numbers and linear algebra introduced in short interludes. Burrell agrees that the mathematics needed does not extend much beyond complex numbers, basic calculus and linear algebra, which are explained in the text.

A practical plan:

• Work in order. The chapters build on each other, so do not skip the early state and principle chapters even if the material seems familiar.
• Do the exercises. The publisher stresses them, and the mathematics only sticks when used.
• Linger on entanglement. Chapters 6 and 7 are the distinctive part; read them slowly.
• Move on. After Chapter 10, continue with a textbook such as Rae and Napolitano or Griffiths for angular momentum, approximations and scattering.