Introduction to Quantum Mechanics

Description

Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials. >Provides clear and accessible explanations of the foundations of quantum mechanics, using an attractive and informal style >It is thorough, with an appropriate amount of mathematical rigor and a good variety of examples and problems >Students emerge with a confident understanding of what the theory says and how to apply it, a solid foundation for more advanced work, and an appreciation for one of the greatest products of the human mind Cover Overview Title page Copyright Contents (direct linking) Preface 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 Schröger 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 Varitional 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 (direct linking) A B C D E F G H I J K L M N O P Q R S T U V W Y Z ErrataIQM3