Introduction to Quantum Mechanics

646 Pages·2018·25.228 MB·English

by  David J. Griffiths, Darrell F. Schroeter

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INTRODUCTION TO QUANTUM MECHANICS
Third edition
Changes and additions to the new edition of this classic textbook include:
A new chapter on Symmetries and Conservation Laws
New problems and examples
Improved explanations
More numerical problems to be worked on a computer
New applications to solid state physics
Consolidated treatment of time-dependent potentials
David J. Griffiths received his BA (1964) and PhD (1970) from Harvard University. He taught at Hampshire
College, Mount Holyoke College, and Trinity College before joining the faculty at Reed College in 1978. In
2001–2002 he was visiting Professor of Physics at the Five Colleges (UMass, Amherst, Mount Holyoke,
Smith, and Hampshire), and in the spring of 2007 he taught Electrodynamics at Stanford. Although his PhD
was in elementary particle theory, most of his research is in electrodynamics and quantum mechanics. He is
the author of over fifty articles and four books: Introduction to Electrodynamics (4th edition, Cambridge
University Press, 2013), Introduction to Elementary Particles (2nd edition, Wiley-VCH, 2008), Introduction to
Quantum Mechanics (2nd edition, Cambridge, 2005), and Revolutions in Twentieth-Century Physics
(Cambridge, 2013).
Darrell F. Schroeter is a condensed matter theorist. He received his BA (1995) from Reed College and his
PhD (2002) from Stanford University where he was a National Science Foundation Graduate Research
Fellow. Before joining the Reed College faculty in 2007, Schroeter taught at both Swarthmore College and
Occidental College. His record of successful theoretical research with undergraduate students was recognized
in 2011 when he was named as a KITP-Anacapa scholar.
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INTRODUCTION TO QUANTUM
MECHANICS
Third edition
DAVID J. GRIFFITHS and DARRELL F. SCHROETER
Reed College, Oregon
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www.cambridge.org
Information on this title: www.cambridge.org/9781107189638
DOI: 10.1017/9781316995433
Second edition © David Griffiths 2017
Third edition © Cambridge University Press 2018
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no
reproduction of any part may take place without the written permission of Cambridge University Press.
This book was previously published by Pearson Education, Inc. 2004
Second edition reissued by Cambridge University Press 2017
Third edition 2018
Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall, 2018
A catalogue record for this publication is available from the British Library.
Library of Congress Cataloging-in-Publication Data
Names: Griffiths, David J. | Schroeter, Darrell F.
Title: Introduction to quantum mechanics / David J. Griffiths (Reed College, Oregon), Darrell F. Schroeter (Reed College, Oregon).
Description: Third edition. | blah : Cambridge University Press, 2018.
Identifiers: LCCN 2018009864 | ISBN 9781107189638
Subjects: LCSH: Quantum theory.
Classification: LCC QC174.12 .G75 2018 | DDC 530.12–dc23
LC record available at https://lccn.loc.gov/2018009864
ISBN 978-1-107-18963-8 Hardback
Additional resources for this publication at www.cambridge.org/IQM3ed
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites
referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
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Contents
Preface
I Theory
1The Wave Function
1.1The Schrödinger Equation
1.2The Statistical Interpretation
1.3Probability
1.3.1Discrete Variables
1.3.2Continuous Variables
1.4Normalization
1.5Momentum
1.6The Uncertainty Principle
Further Problems on Chapter 1
2Time-Independent Schrödinger Equation
2.1Stationary States
2.2The Infinite Square Well
2.3The Harmonic Oscillator
2.3.1Algebraic Method
2.3.2Analytic Method
2.4The Free Particle
2.5The Delta-Function Potential
2.5.1Bound States and Scattering States
2.5.2The Delta-Function Well
2.6The Finite Square Well
Further Problems on Chapter 2
3Formalism
3.1Hilbert Space
3.2Observables
3.2.1Hermitian Operators
3.2.2Determinate States
3.3Eigenfunctions of a Hermitian Operator
3.3.1Discrete Spectra
3.3.2Continuous Spectra
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3.4Generalized Statistical Interpretation
3.5The Uncertainty Principle
3.5.1Proof of the Generalized Uncertainty Principle
3.5.2The Minimum-Uncertainty Wave Packet
3.5.3The Energy-Time Uncertainty Principle
3.6Vectors and Operators
3.6.1Bases in Hilbert Space
3.6.2Dirac Notation
3.6.3Changing Bases in Dirac Notation
Further Problems on Chapter 3
4Quantum Mechanics in Three Dimensions
4.1The Schröger Equation
4.1.1Spherical Coordinates
4.1.2The Angular Equation
4.1.3The Radial Equation
4.2The Hydrogen Atom
4.2.1The Radial Wave Function
4.2.2The Spectrum of Hydrogen
4.3Angular Momentum
4.3.1Eigenvalues
4.3.2Eigenfunctions
4.4Spin
4.4.1Spin 1/2
4.4.2Electron in a Magnetic Field
4.4.3Addition of Angular Momenta
4.5Electromagnetic Interactions
4.5.1Minimal Coupling
4.5.2The Aharonov–Bohm Effect
Further Problems on Chapter 4
5Identical Particles
5.1Two-Particle Systems
5.1.1Bosons and Fermions
5.1.2Exchange Forces
5.1.3Spin
5.1.4Generalized Symmetrization Principle
5.2Atoms
5.2.1Helium
5.2.2The Periodic Table
5.3Solids
5.3.1The Free Electron Gas
5.3.2Band Structure
Further Problems on Chapter 5
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6Symmetries & Conservation Laws
6.1Introduction
6.1.1Transformations in Space
6.2The Translation Operator
6.2.1How Operators Transform
6.2.2Translational Symmetry
6.3Conservation Laws
6.4Parity
6.4.1Parity in One Dimension
6.4.2Parity in Three Dimensions
6.4.3Parity Selection Rules
6.5Rotational Symmetry
6.5.1Rotations About the z Axis
6.5.2Rotations in Three Dimensions
6.6Degeneracy
6.7Rotational Selection Rules
6.7.1Selection Rules for Scalar Operators
6.7.2Selection Rules for Vector Operators
6.8Translations in Time
6.8.1The Heisenberg Picture
6.8.2Time-Translation Invariance
Further Problems on Chapter 6
II Applications
7Time-Independent Perturbation Theory
7.1Nondegenerate Perturbation Theory
7.1.1General Formulation
7.1.2First-Order Theory
7.1.3Second-Order Energies
7.2Degenerate Perturbation Theory
7.2.1Two-Fold Degeneracy
7.2.2“Good” States
7.2.3Higher-Order Degeneracy
7.3The Fine Structure of Hydrogen
7.3.1The Relativistic Correction
7.3.2Spin-Orbit Coupling
7.4The Zeeman Effect
7.4.1Weak-Field Zeeman Effect
7.4.2Strong-Field Zeeman Effect
7.4.3Intermediate-Field Zeeman Effect
7.5Hyperfine Splitting in Hydrogen
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Further Problems on Chapter 7
8The Varitional Principle
8.1Theory
8.2The Ground State of Helium
8.3The Hydrogen Molecule Ion
8.4The Hydrogen Molecule
Further Problems on Chapter 8
9The WKB Approximation
9.1The “Classical” Region
9.2Tunneling
9.3The Connection Formulas
Further Problems on Chapter 9
10Scattering
10.1Introduction
10.1.1Classical Scattering Theory
10.1.2Quantum Scattering Theory
10.2Partial Wave Analysis
10.2.1Formalism
10.2.2Strategy
10.3Phase Shifts
10.4The Born Approximation
10.4.1Integral Form of the Schrödinger Equation
10.4.2The First Born Approximation
10.4.3The Born Series
Further Problems on Chapter 10
11Quantum Dynamics
11.1Two-Level Systems
11.1.1The Perturbed System
11.1.2Time-Dependent Perturbation Theory
11.1.3Sinusoidal Perturbations
11.2Emission and Absorption of Radiation
11.2.1Electromagnetic Waves
11.2.2Absorption, Stimulated Emission, and Spontaneous Emission
11.2.3Incoherent Perturbations
11.3Spontaneous Emission
11.3.1Einstein’s A and B Coefficients
11.3.2The Lifetime of an Excited State
11.3.3Selection Rules
11.4Fermi’s Golden Rule
11.5The Adiabatic Approximation
11.5.1Adiabatic Processes
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11.5.2The Adiabatic Theorem
Further Problems on Chapter 11
12Afterword
12.1The EPR Paradox
12.2Bell’s Theorem
12.3Mixed States and the Density Matrix
12.3.1Pure States
12.3.2Mixed States
12.3.3Subsystems
12.4The No-Clone Theorem
12.5Schrödinger’s Cat
Appendix Linear Algebra
A.1Vectors
A.2Inner Products
A.3Matrices
A.4Changing Bases
A.5Eigenvectors and Eigenvalues
A.6Hermitian Transformations
Index
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