Introduction to Quantum Mechanics 3rd Edition by David J Griffiths, Darrell F Schroeter ISBN 1107189632 9781107189638

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ISBN 10: 1107189632
ISBN 13: 9781107189638
Author: David J Griffiths, Darrell F Schroeter

Introduction to Quantum Mechanics 3rd Edition Table of contents:

Part I Theory

1 The Wave Function

1.1 The Schrödinger Equation

1.2 The Statistical Interpretation

1.3 Probability

1.3.1 Discrete Variables

1.3.2 Continuous Variables

1.4 Normalization

1.5 Momentum

1.6 The Uncertainty Principle

Further Problems on Chapter 1

2 Time-Independent Schrödinger Equation

2.1 Stationary States

2.2 The Infinite Square Well

2.3 The Harmonic Oscillator

2.3.1 Algebraic Method

2.3.2 Analytic Method

2.4 The Free Particle

2.5 The Delta-Function Potential

2.5.1 Bound States and Scattering States

2.5.2 The Delta-Function Well

2.6 The Finite Square Well

Further Problems on Chapter 2

3 Formalism

3.1 Hilbert Space

3.2 Observables

3.2.1 Hermitian Operators

3.2.2 Determinate States

3.3 Eigenfunctions of a Hermitian Operator

3.3.1 Discrete Spectra

3.3.2 Continuous Spectra

3.4 Generalized Statistical Interpretation

3.5 The Uncertainty Principle

3.5.1 Proof of the Generalized Uncertainty Principle

3.5.2 The Minimum-Uncertainty Wave Packet

3.5.3 The Energy-Time Uncertainty Principle

3.6 Vectors and Operators

3.6.1 Bases in Hilbert Space

3.6.2 Dirac Notation

3.6.3 Changing Bases in Dirac Notation

Further Problems on Chapter 3

4 Quantum Mechanics in Three Dimensions

4.1 The Schrödinger Equation

4.1.1 Spherical Coordinates

4.1.2 The Angular Equation

4.1.3 The Radial Equation

4.2 The Hydrogen Atom

4.2.1 The Radial Wave Function

4.2.2 The Spectrum of Hydrogen

4.3 Angular Momentum

4.3.1 Eigenvalues

4.3.2 Eigenfunctions

4.4 Spin

4.4.1 Spin 1/2

4.4.2 Electron in a Magnetic Field

4.4.3 Addition of Angular Momenta

4.5 Electromagnetic Interactions

4.5.1 Minimal Coupling

4.5.2 The Aharonov–Bohm Effect

Further Problems on Chapter 4

5 Identical Particles

5.1 Two-Particle Systems

5.1.1 Bosons and Fermions

5.1.2 Exchange Forces

5.1.3 Spin

5.1.4 Generalized Symmetrization Principle

5.2 Atoms

5.2.1 Helium

5.2.2 The Periodic Table

5.3 Solids

5.3.1 The Free Electron Gas

5.3.2 Band Structure

Further Problems on Chapter 5

6 Symmetries & Conservation Laws

6.1 Introduction

6.1.1 Transformations in Space

6.2 The Translation Operator

6.2.1 How Operators Transform

6.2.2 Translational Symmetry

6.3 Conservation Laws

6.4 Parity

6.4.1 Parity in One Dimension

6.4.2 Parity in Three Dimensions

6.4.3 Parity Selection Rules

6.5 Rotational Symmetry

6.5.1 Rotations About the z Axis

6.5.2 Rotations in Three Dimensions

6.6 Degeneracy

6.7 Rotational Selection Rules

6.7.1 Selection Rules for Scalar Operators

6.7.2 Selection Rules for Vector Operators

6.8 Translations in Time

6.8.1 The Heisenberg Picture

6.8.2 Time-Translation Invariance

Further Problems on Chapter 6

Part II Applications

7 Time-Independent Perturbation Theory

7.1 Nondegenerate Perturbation Theory

7.1.1 General Formulation

7.1.2 First-Order Theory

7.1.3 Second-Order Energies

7.2 Degenerate Perturbation Theory

7.2.1 Two-Fold Degeneracy

7.2.2 “Good” States

7.2.3 Higher-Order Degeneracy

7.3 The Fine Structure of Hydrogen

7.3.1 The Relativistic Correction

7.3.2 Spin-Orbit Coupling

7.4 The Zeeman Effect

7.4.1 Weak-Field Zeeman Effect

7.4.2 Strong-Field Zeeman Effect

7.4.3 Intermediate-Field Zeeman Effect

7.5 Hyperfine Splitting in Hydrogen

Further Problems on Chapter 7

8 The Variational Principle

8.1 Theory

8.2 The Ground State of Helium

8.3 The Hydrogen Molecule Ion

8.4 The Hydrogen Molecule

Further Problems on Chapter 8

9 The WKB Approximation

9.1 The “Classical” Region

9.2 Tunneling

9.3 The Connection Formulas

Further Problems on Chapter 9

10 Scattering

10.1 Introduction

10.1.1 Classical Scattering Theory

10.1.2 Quantum Scattering Theory

10.2 Partial Wave Analysis

10.2.1 Formalism

10.2.2 Strategy

10.3 Phase Shifts

10.4 The Born Approximation

10.4.1 Integral Form of the Schrödinger Equation

10.4.2 The First Born Approximation

10.4.3 The Born Series

Further Problems on Chapter 10

11 Quantum Dynamics

11.1 Two-Level Systems

11.1.1 The Perturbed System

11.1.2 Time-Dependent Perturbation Theory

11.1.3 Sinusoidal Perturbations

11.2 Emission and Absorption of Radiation

11.2.1 Electromagnetic Waves

11.2.2 Absorption, Stimulated Emission, and Spontaneous Emission

11.2.3 Incoherent Perturbations

11.3 Spontaneous Emission

11.3.1 Einstein’s A and B Coefficients

11.3.2 The Lifetime of an Excited State

11.3.3 Selection Rules

11.4 Fermi’s Golden Rule

11.5 The Adiabatic Approximation

11.5.1 Adiabatic Processes

11.5.2 The Adiabatic Theorem

Further Problems on Chapter 11

12 Afterword

12.1 The EPR Paradox

12.2 Bell’s Theorem

12.3 Mixed States and the Density Matrix

12.3.1 Pure States

12.3.2 Mixed States

12.3.3 Subsystems

12.4 The No-Clone Theorem

12.5 Schrödinger’s Cat

Appendix Linear Algebra

A.1 Vectors

A.2 Inner Products

A.3 Matrices

A.4 Changing Bases

A.5 Eigenvectors and Eigenvalues

A.6 Hermitian Transformations

Index

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Tags: David J Griffiths, Darrell F Schroeter, Quantum Mechanics, Introduction