Introduction to Quantum Mechanics

Citation

Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.

Chapter Summary

The third edition has twelve chapters in two parts, an appendix on linear algebra and about 500 pages in all. Part I (Chapters 1–6) is the basic theory; Part II (Chapters 7–12) collects approximation methods, applications and a closing look at foundations. Problems sit at the end of sections and chapters, graded with stars.

Chapter 1: The Wave Function

The Schrödinger equation, the statistical interpretation of the wave function, probability for discrete and continuous variables, normalization, momentum, and the uncertainty principle. This is the only background chapter; the preface saves deeper questions of meaning for the end.

Chapter 2: Time-Independent Schrödinger Equation

Stationary states and the standard solvable potentials: the infinite square well, the harmonic oscillator (by an algebraic and by an analytic method), the free particle, the delta-function potential with bound and scattering states, and the finite square well.

Chapter 3: Formalism

Hilbert space, observables and Hermitian operators, determinate states, eigenfunctions with discrete and continuous spectra, the generalized statistical interpretation, the generalized uncertainty principle (including the energy-time version), and vectors and operators with Dirac notation.

Chapter 4: Quantum Mechanics in Three Dimensions

The Schrödinger equation in spherical coordinates, the hydrogen atom and its spectrum, angular momentum, spin (spin 1/2, an electron in a magnetic field, addition of angular momenta), and electromagnetic interactions including minimal coupling and the Aharonov-Bohm effect.

Chapter 5: Identical Particles

Two-particle systems, bosons and fermions, exchange forces, spin and the generalized symmetrization principle; atoms (helium and the periodic table); and solids (the free electron gas and band structure).

Chapter 6: Symmetries & Conservation Laws

New in the third edition and written largely by Schroeter. Transformations in space, the translation operator and translational symmetry, conservation laws, parity and its selection rules, rotational symmetry, degeneracy, rotational selection rules for scalar and vector operators, and translations in time with the Heisenberg picture.

Chapter 7: Time-Independent Perturbation Theory

Nondegenerate and degenerate perturbation theory, then applications to hydrogen: fine structure (relativistic correction and spin-orbit coupling), the Zeeman effect at weak, strong and intermediate fields, and hyperfine splitting.

Chapter 8: The Variational Principle

The variational method in theory, then the ground state of helium, the hydrogen molecule ion and the hydrogen molecule.

Chapter 9: The WKB Approximation

The "classical" region, tunneling, and the connection formulas.

Chapter 10: Scattering

Classical and quantum scattering theory, partial wave analysis, phase shifts, and the Born approximation including the Born series.

Chapter 11: Quantum Dynamics

Two-level systems and time-dependent perturbation theory, sinusoidal perturbations, absorption, stimulated and spontaneous emission with Einstein's A and B coefficients, selection rules, Fermi's golden rule, and the adiabatic approximation, which absorbs the earlier edition's separate chapter on it.

Chapter 12: Afterword

The EPR paradox, Bell's theorem, mixed states and the density matrix, the no-clone theorem, and Schrödinger's cat.

Appendix: Linear Algebra

Vectors, inner products, matrices, changes of basis, eigenvectors and eigenvalues, and Hermitian transformations.

Key Concepts

Chapters 1–3: Wave Function and Formalism

• Statistical interpretation: the squared magnitude of the wave function gives a probability density.
• Stationary states: separable solutions of definite energy that underlie the solvable examples of Chapter 2.
• Hermitian operators and eigenvalues: the mathematical form of observables and their possible measured values.
• Generalized uncertainty principle: a bound on the product of uncertainties for any two observables.

Chapters 4–6: Three Dimensions, Identical Particles, Symmetry

• Angular momentum and spin: orbital and intrinsic angular momentum, and how they add.
• Bosons and fermions: symmetric and antisymmetric states for identical particles.
• Symmetry and conservation: translation, parity and rotation, with the selection rules they imply.

Chapters 7–11: Approximation Methods and Dynamics

• Perturbation theory: small corrections to exactly solvable systems.
• Variational principle: an upper bound on the ground-state energy from trial wave functions.
• WKB approximation: semiclassical treatment of tunneling and slowly varying potentials.
• Born approximation and partial waves: two ways to compute scattering amplitudes.
• Fermi's golden rule: the rate of transitions induced by a perturbation.

Chapter 12: Foundations

• Bell's theorem and the EPR paradox: the argument that quantum correlations cannot be reproduced by local hidden variables.
• Density matrix: the description of mixed states and subsystems.

Critical Analysis

Strengths

• A clear stated purpose. The authors say the book is meant "to teach you how to do quantum mechanics", leaving questions of interpretation to the Afterword, which readers who cannot wait may take up right after Chapter 1.
• A flexible two-part design. Part I is the core theory and Part II is a toolkit of approximation methods; the preface says the parts need not be studied in the order printed and suggests, for example, perturbation theory right after Chapter 2. The book fits a one-semester course (mostly Part I) or a full year.
• Graded problems. The preface rates problems with stars (one for essential, two for more difficult or peripheral, three for unusually challenging) and marks those that need a computer. Because the text contains fewer worked examples than is customary, the problems carry real teaching content.
• A tight third edition. The new Chapter 6 on symmetries, new applications to solid-state physics, and a consolidated treatment of time-dependent potentials were added while the adiabatic chapter and statistical mechanics material were removed so that the book would not "grow fat".

Limitations

• Few worked examples. The authors acknowledge that readers have noted fewer examples than usual and that important material sits in the problems. Self-studying readers will need to do the problems, and the solution manual is available to instructors only.
• Mathematical demands. The preface lists Legendre, Hermite and Laguerre polynomials, spherical harmonics, Bessel and Airy functions, Hilbert spaces and Clebsch-Gordan coefficients. Readers are expected to know linear algebra basics, complex numbers and calculus through partial derivatives, plus classical mechanics.
• Nonrelativistic scope. The topics stop at the nonrelativistic theory of a few particles, with relativity entering only as corrections in hydrogen's fine structure; the book does not go on to field theory.
• Conceptual questions come last. Readers drawn to interpretation will find only one short chapter on it.

Where It Fits in the Course

Griffiths and Schroeter is the standard-format junior or senior text in this quantum mechanics list. Rae and Napolitano's Quantum Mechanics is a more compact first undergraduate course that develops wave mechanics from the experimental evidence. Susskind and Friedman's Quantum Mechanics: The Theoretical Minimum starts from spin and two-state systems rather than wave mechanics, and suits readers who want the logic and mathematics before a full course. David Albert's Quantum Mechanics and Experience is a conceptual guide to states, measurement and nonlocality that can be read alongside Chapter 12 or Chapter 1.

Sakurai and Napolitano's Modern Quantum Mechanics is the mathematically mature next step: it uses Dirac notation to develop states, angular momentum, symmetries, approximations and scattering at an advanced undergraduate and beginning graduate level. Chapter 3's Dirac notation and Chapter 6's symmetries introduce topics that Sakurai develops at greater length.

How to Use This Book

The book is for physics, chemistry and engineering students who have taken classical mechanics, linear algebra and multivariable calculus, and have met some electrodynamics. Use Appendix A as a refresher on linear algebra.

A practical plan:

• One-semester core: Chapters 1–4 in order, then the parts of Chapter 5 that interest you; Chapter 6 if time allows.
• Approximation toolbox: Chapters 7 and 8 (perturbation and variational methods) are the first tools of Part II. Choose among Chapters 9–11 according to the topic you need: tunneling, scattering or radiation.
• Foundations: the Afterword can be read after Chapter 1 or Chapter 3, as the preface invites.

Do the problems, starting with the single-star ones, which the authors place mostly at the ends of sections, and attempt the three-star problems at chapter ends once the chapter is clear. Use the computer problems to build intuition for wave functions and the numerical solution of the Schrödinger equation. When a mathematical tool is unfamiliar, the preface recommends Boas's Mathematical Methods in the Physical Sciences or Arfken, Weber and Harris's Mathematical Methods for Physicists.