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Quantum Mechanics cover

Physics

Physics

Quantum Mechanics

Alastair I. M. Rae; Jim Napolitano

A compact introductory textbook for a first undergraduate course in quantum mechanics, long used in Britain and revised for this edition with a second author. It develops wave mechanics from the experimental evidence, then introduces operators, angular momentum and spin, approximation methods and many-particle systems, and ends by discussing what quantum theory says about measurement and reality.

Prerequisites: Calculus, ordinary differential equations, complex numbers and introductory waves; some linear algebra helps.

Difficulty Level
Intermediate
Academic Level
Undergraduate
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01 / Reading Guide

Reading Guide

Citation

Rae, A. I. M., & Napolitano, J. (2015). Quantum Mechanics (6th ed.). CRC Press.

Chapter Summary

The sixth edition runs to about 440 pages (xxiv + 413) and, for the first time, is divided into five parts with sixteen chapters; every chapter ends with problems. Alastair Rae, a retired reader in quantum physics at the University of Birmingham, first taught the subject in the 1970s, which led to the first edition; Jim Napolitano, an experimental nuclear and particle physicist at Temple University, joins him for this edition. According to the publisher, the edition adds three chapters reviewing prerequisite physics and mathematics, short descriptions of applications, and more end-of-chapter problems of varied difficulty.

Part I, Chapters 1–4: The Physics and Mathematics of Waves; Maxwell's Equations and Electromagnetic Waves; Particle Mechanics, Relativity, and Photons; The Early Development of Quantum Mechanics

The new review part. Chapter 1 covers simple harmonic motion, the stretched-string equation, standing waves and Fourier series, and the Fourier transform. Chapter 2 presents Maxwell's equations as integrals and as derivatives, with the vector-calculus surface theorems, and electromagnetic waves and radiation. Chapter 3 reviews spacetime, momentum and energy in special relativity. Chapter 4 turns to the evidence for quantum theory: the photoelectric and Compton effects, line spectra, de Broglie waves and wave-particle duality, and closes with an outline of the rest of the book.

Part II, Chapters 5–6: The One-Dimensional Schrödinger Equations; The Three-Dimensional Schrödinger Equations

The time-dependent and time-independent equations, boundary conditions, infinite and finite square wells, tunnelling and the harmonic oscillator; then separation of variables in Cartesian and spherical polar coordinates, leading to the hydrogenic atom.

Part III, Chapters 7–9: The Basic Postulates of Quantum Mechanics; Angular Momentum I; Angular Momentum II

Chapter 7 states the postulates: wave function, operators for dynamical variables, probability distributions, commutation relations, the uncertainty principle, time dependence and degeneracy, revisiting the harmonic oscillator and analysing the measurement of momentum by Compton scattering. Chapter 8 treats angular-momentum operators, eigenvalues and eigenfunctions, experimental measurement and a general solution of the eigenvalue problem. Chapter 9 introduces matrix representations, Pauli spin matrices, spin and measurement, Dirac notation, spin-orbit coupling and the Zeeman effect, and the coupling of angular momenta.

Part IV, Chapters 10–13: Time-Independent Perturbation Theory and the Variational Principle; Time Dependence; Scattering; Many-Particle Systems

Perturbation theory for non-degenerate and degenerate levels and the variational principle; time-independent Hamiltonians, the sudden approximation, time-dependent perturbation theory, atomic transitions, the Ehrenfest theorem and the ammonia maser; scattering in one and three dimensions, the Born approximation and partial-wave analysis; and indistinguishable particles, many-particle systems, the helium atom and scattering of identical particles.

Part V, Chapters 14–16: Relativity and Quantum Mechanics; Quantum Information; The Conceptual Problems of Quantum Mechanics

Chapter 14 introduces the Dirac equation, antiparticles, other wave equations, and quantum field theory with the spin-statistics theorem. Chapter 15 covers quantum cryptography, entanglement, cloning and teleportation, and quantum computing. Chapter 16, the longest of the part, examines hidden-variable theories, nonlocality, the measurement problem and the ontological problem.

Key Concepts

Parts I–II: Foundations and wave mechanics

  • Fourier transform: decomposing a wave into components of different wavelength, reviewed in Chapter 1 alongside Fourier series.
  • Wave-particle duality: the evidence that light and matter show both wave and particle behaviour.
  • Tunnelling: penetration of a particle through a barrier that is classically forbidden.
  • Hydrogenic atom: the energy levels and wave functions found by separating the Schrödinger equation in spherical polar coordinates.

Part III: Formalism

  • Postulates: the rules connecting wave functions and operators to measurement outcomes.
  • Commutation relations and uncertainty: non-commuting observables cannot be simultaneously sharp.
  • Spin and Pauli matrices: an intrinsic angular momentum represented by 2×2 matrices.
  • Dirac notation: the bra-ket notation for states and operators.

Parts IV–V: Approximations and advanced topics

  • Perturbation theory and the variational principle: methods for estimating energies when exact solutions are unavailable.
  • Born approximation and partial waves: two approaches to scattering cross sections.
  • Indistinguishable particles: the symmetry requirements that underlie the helium atom and identical-particle scattering.
  • Entanglement and nonlocality: correlations at the heart of quantum information and of the conceptual problems in Chapter 16.

Critical Analysis

Strengths

  • A built-in review of prerequisites. Part I reviews waves, Fourier methods, Maxwell's equations and relativity. Reviewers quoted by the publisher (V. F. Mitrovic, Brown University; Pete Markowitz, Florida International University) single this out as useful for students with a weaker background, noting that Maxwell's equations are often left out of competing books.
  • Modular structure. Francesco Montalenti, reviewing the book in Il Nuovo Saggiatore (2017), notes that the five parts help teachers select topics to suit their students; Robert Pelcovits (Brown University) calls the book versatile, from an honours introductory course to an upper-level one.
  • Applications alongside theory. Short asides on applications, among them magnetic resonance imaging, electron and scanning tunnelling microscopy and superconductivity, according to quoted reviewers, show what quantum mechanics has made possible.
  • Strong final chapters. Montalenti found Chapter 15 an accessible introduction to quantum cryptography, computing and teleportation with worked examples, and Chapter 16 an in-depth analysis of quantum measurement, including its philosophical consequences.

Limitations

  • Wave mechanics before formalism. Dirac notation arrives only in Chapter 9; students heading for a course built on state vectors from the start will need to bridge the gap.
  • Part I may be redundant. For students who have already taken waves, electromagnetism and relativity courses, the first four chapters (about 80 pages) can be skimmed.
  • Evidence on difficulty is mixed. Reviewers describe it as suitable for a senior-level course and as a good choice for students entering graduate engineering programmes, so it is not a first-year text despite its review part.

Where It Fits in the Course

Within this quantum mechanics list, Rae and Napolitano sit alongside Griffiths's Introduction to Quantum Mechanics as a main undergraduate text. Both cover wave mechanics, formalism, angular momentum and approximation methods; Rae and Napolitano add the review part, more on quantum information, and a long chapter on conceptual problems. Susskind and Friedman's Quantum Mechanics: The Theoretical Minimum takes the opposite route, starting from spin and two-state systems rather than wave mechanics, and is a good companion for Chapters 7–9. David Albert's Quantum Mechanics and Experience is a conceptual guide to measurement and nonlocality that pairs naturally with Chapter 16. Sakurai and Napolitano's Modern Quantum Mechanics, which shares a co-author, is the step beyond, built on Dirac notation from the start.

How to Use This Book

The book suits students in their second or third year of a physics degree, and students in chemistry, materials science or engineering, who have calculus, differential equations and complex numbers. Linear algebra helps from Chapter 9 onwards.

  • Prepare: skim Part I, reading closely only the chapters on topics not yet studied; Chapter 4 is worth reading in any case as motivation.
  • Core: Parts II and III (Chapters 5–9), the heart of a first course.
  • Second course or later weeks: Part IV, with perturbation theory (Chapter 10) and time dependence (Chapter 11) first, then scattering and many-particle systems.
  • Advanced reading: Part V, chosen by interest: Chapter 14 for relativistic quantum theory, Chapter 15 for quantum information, Chapter 16 for interpretation.

Work several end-of-chapter problems in each chapter, choosing across the range of difficulty the new edition provides, and redo the worked examples without looking at the solution first.