Introduction to Quantum Mechanics 3rd Edition

Introduction to Quantum Mechanics 3rd Edition | ISBN-13 9781107189638

Introduction to Quantum Mechanics, 3rd Edition is a highly regarded textbook that has been extensively updated to provide a deeper and more comprehensive understanding of quantum mechanics. This edition includes a new chapter on symmetries, along with improved explanations, additional examples, and an expanded set of problems, including more numerical problems designed to be solved using computers. These enhancements make the textbook even more valuable for students and professionals looking to master the fundamental principles of quantum mechanics.

The book retains its clear and accessible approach, making complex topics in quantum mechanics more understandable. With applications to solid-state physics and a consolidated treatment of time-dependent potentials, this edition continues to bridge the gap between theory and practical applications, preparing students for advanced study and research in the field.

Key Features:

• New Chapter on Symmetries: Explores the role of symmetries in quantum mechanics, providing a deeper understanding of fundamental principles.
• Expanded Problems and Examples: Includes more numerical problems suitable for computer-based solutions, along with new examples to reinforce learning.
• Improved Explanations: Enhanced clarity in explanations to help students grasp complex quantum mechanics concepts more effectively.
• Applications to Solid-State Physics: Introduces real-world applications, demonstrating the relevance of quantum mechanics in various fields of physics.
• Consolidated Treatment of Time-Dependent Potentials: Provides a more integrated approach to this critical aspect of quantum mechanics.

Table of Contents:

Front Matter:

• Front Endpapers
• Half-title page
• Title page
• Copyright page
• Contents
• Preface

Part I: Theory

1. The Wave Function
   • The Schrödinger Equation
   • The Statistical Interpretation
   • Probability (Discrete and Continuous Variables)
   • Normalization
   • Momentum
   • The Uncertainty Principle
   • Further Problems on Chapter 1
2. Time-Independent Schrödinger Equation
   • Stationary States
   • The Infinite Square Well
   • The Harmonic Oscillator (Algebraic and Analytic Methods)
   • The Free Particle
   • The Delta-Function Potential (Bound and Scattering States)
   • The Finite Square Well
   • Further Problems on Chapter 2
3. Formalism
   • Hilbert Space
   • Observables (Hermitian Operators, Determinate States)
   • Eigenfunctions of a Hermitian Operator (Discrete and Continuous Spectra)
   • Generalized Statistical Interpretation
   • The Uncertainty Principle (Proof, Minimum-Uncertainty Wave Packet, Energy-Time Uncertainty)
   • Vectors and Operators (Bases in Hilbert Space, Dirac Notation)
   • Further Problems on Chapter 3
4. Quantum Mechanics in Three Dimensions
   • The Schrödinger Equation in Spherical Coordinates
   • The Hydrogen Atom (Radial Wave Function, Spectrum)
   • Angular Momentum (Eigenvalues, Eigenfunctions)
   • Spin (Spin 1/2, Electron in a Magnetic Field, Addition of Angular Momenta)
   • Electromagnetic Interactions (Minimal Coupling, Aharonov–Bohm Effect)
   • Further Problems on Chapter 4
5. Identical Particles
   • Two-Particle Systems (Bosons and Fermions, Exchange Forces)
   • Atoms (Helium, The Periodic Table)
   • Solids (The Free Electron Gas, Band Structure)
   • Further Problems on Chapter 5
6. Symmetries & Conservation Laws
   • Introduction to Transformations in Space
   • The Translation Operator
   • Conservation Laws
   • Parity (One Dimension, Three Dimensions, Selection Rules)
   • Rotational Symmetry (Rotations About the z Axis, Rotations in Three Dimensions, Degeneracy, Selection Rules)
   • Translations in Time (Heisenberg Picture, Time-Translation Invariance)
   • Further Problems on Chapter 6

Part II: Applications 7. Time-Independent Perturbation Theory

• Nondegenerate and Degenerate Perturbation Theory
• The Fine Structure of Hydrogen (Relativistic Correction, Spin-Orbit Coupling)
• The Zeeman Effect (Weak, Strong, Intermediate-Field)
• Hyperfine Splitting in Hydrogen
• Further Problems on Chapter 7

8. The Variational Principle
   • Theory
   • The Ground State of Helium
   • The Hydrogen Molecule Ion
   • The Hydrogen Molecule
   • Further Problems on Chapter 8
9. The WKB Approximation
   • The “Classical” Region
   • Tunneling
   • The Connection Formulas
   • Further Problems on Chapter 9
10. Scattering

• Classical and Quantum Scattering Theory
• Partial Wave Analysis
• Phase Shifts
• The Born Approximation (Integral Form of the Schrödinger Equation, Born Series)
• Further Problems on Chapter 10

11. Quantum Dynamics

• Two-Level Systems (Time-Dependent Perturbation Theory, Sinusoidal Perturbations)
• Emission and Absorption of Radiation (Electromagnetic Waves, Absorption, Stimulated and Spontaneous Emission, Einstein’s A and B Coefficients, Selection Rules)
• Fermi’s Golden Rule
• The Adiabatic Approximation
• Further Problems on Chapter 11

12. Afterword

• The EPR Paradox
• Bell’s Theorem
• Mixed States and the Density Matrix
• The No-Clone Theorem
• Schrödinger’s Cat

Appendix: Linear Algebra

• Vectors
• Inner Products
• Matrices
• Changing Bases
• Eigenvectors and Eigenvalues
• Hermitian Transformations

Back Matter:

• Index
• Back Endpapers