Fundamentals of Quantum Mechanics

Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models—including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom—are clearly and completely presented. Applications of these models to selected “real world” topics are also included.

This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.

• Accessible style and colorful illustrations make the content appropriate for professional researchers and students alike
• Presents results of quantum mechanical calculations that can be performed with readily available software
• Provides exceptionally clear discussions of spin-orbit coupling and group theory, and comprehensive coverage of barrier penetration (quantum mechanical tunneling) that touches upon hot topics, such as superconductivity and scanning tunneling microscopy
• Problems given at the end of each chapter help students to master concepts

Upper-level undergraduate students and graduate students studying quantum mechanics in chemistry or physics; organic chemists using quantum chemistry in their research

Chapter 1: Origins of Quantum Theory

• Abstract
• 1.1 Blackbody Radiation
• 1.2 The Line Spectrum of Atomic Hydrogen
• 1.3 Electrons and the Nucleus
• 1.4 The Bohr Model for the Hydrogen Atom
• 1.5 The Photoelectric Effect
• 1.6 Particle-Wave Duality
• 1.7 The Heisenberg Uncertainty Principle
• Problems

Chapter 2: The Methods of Quantum Mechanics

• Abstract
• 2.1 The Postulates
• 2.2 The Wave Equation
• 2.3 Operators
• 2.4 Eigenvalues
• 2.5 Wave Functions
• Problems

Chapter 3: Particles in Boxes

• Abstract
• 3.1 The Particle in a One-Dimensional Box
• 3.2 Separation of Variables
• 3.3 The Particle in a Three-Dimensional Box
• 3.4 F-Centers in Crystals
• 3.5 Solvated Electrons
• Problems

Chapter 4: The Hydrogen Atom

• Abstract
• 4.1 Schrödinger′s Solution to the Hydrogen Atom Problem
• 4.2 Interpreting the Solutions
• 4.3 p and d Wave Functions and Orbitals
• 4.4 Orthogonality
• 4.5 Approximate Wave Functions and the Variation Method
• Problems

Chapter 5: Structure and Properties of More Complex Atoms

• Abstract
• 5.1 The Helium Atom
• 5.2 Perturbation Method
• 5.3 Slater Wave Functions
• 5.4 Electron Configurations
• 5.5 Spectroscopic States
• Problems

Chapter 6: Vibrations and the Harmonic Oscillator

• Abstract
• 6.1 The Vibrating Object
• 6.2 Linear Differential Equations with Constant Coefficients
• 6.3 Back to the Vibrating Object
• 6.4 The Quantum Mechanical Harmonic Oscillator
• 6.5 Series Solutions of Differential Equations
• 6.6 Back to the Harmonic Oscillator
• 6.7 Population of States
• 6.8 Heat Capacity of Metals
• Problems

Chapter 7: Molecular Rotation and Spectroscopy

• Abstract
• 7.1 Rotational Energies
• 7.2 Quantum Mechanics of Rotation
• 7.3 Heat Capacities of Gases
• 7.4 Energy Levels in Gaseous Atoms and Molecules
• 7.5 Rotational Spectra of Diatomic Molecules
• Problems

Chapter 8: Bonding and Properties of Diatomic Molecules

• Abstract
• 8.1 An Elementary Look at Covalent Bonds
• 8.2 Some Simple Relationships for Bonds
• 8.3 The LCAO-MO Method
• 8.4 Diatomic Molecules of the Second Period
• 8.5 Overlap and Exchange Integrals
• 8.6 Heteronuclear Diatomic Molecules
• 8.7 Symmetry of Molecular Orbitals
• 8.8 Orbital Symmetry and Reactivity
• 8.9 Term Symbols
• Problems

Chapter 9: The Hückel Molecular Orbital Method

• Abstract
• 9.1 The Hückel Method
• 9.2 Determinants
• 9.3 Solving Polynomial Equations
• 9.4 Hückel Calculations for Larger Molecules
• 9.5 Calculations Including Heteroatoms
• 9.6 Some Triatomic Inorganic Molecules
• 9.7 Kernels, Repulsion, and Stability
• 9.8 Band Theory of Metals
• Problems

Chapter 10: Molecular Structure and Symmetry

• Abstract
• 10.1 Valence Bond Description of Molecular Structure
• 10.2 What Symmetry Means
• 10.3 Symmetry Elements
• 10.4 What Point Group Is It?
• 10.5 Group Theory
• 10.6 Symmetry of Molecular Orbitals
• 10.7 Molecular Orbital Diagrams
• 10.8 The Three-Center Bond
• 10.9 Orbital Symmetry and Reactivity
• Problems

Chapter 11: Molecular Spectroscopy

• Abstract
• 11.1 Visible and Ultraviolet Spectroscopy
• 11.2 Electronic Transitions in Molecules
• 11.3 Photoelectron Spectroscopy
• 11.4 Determining Bond Lengths in Diatomic Molecules
• 11.5 Structure Determination
• 11.6 Types of Bonds Present
• 11.7 Solvatochromism
• 11.8 The Hydrogen Bond
• 11.9 Effects of Hydrogen Bonding on Spectra
• Problems

Chapter 12: Spectroscopy of Metal Complexes

• Abstract
• 12.1 The Effect of Ligands on d Orbitals
• 12.2 Bands in Electronic Spectra of Complexes
• 12.3 Interpreting Electronic Spectra of Complexes
• 12.4 Charge Transfer Absorption
• 12.5 Back Donation
• Problems

Chapter 13: Barrier Penetration

• Abstract
• 13.1 The Phenomenon of Barrier Penetration
• 13.2 The Wave Equations
• 13.3 Alpha Decay
• 13.4 Tunneling and Superconductivity
• 13.5 The Scanning Tunneling Microscope
• 13.6 Spin Tunneling
• 13.7 Tunneling in Ammonia Inversion
• Problems

Chapter 14: Comments on Computational Methods

• Abstract
• 14.1 The Fundamental Problem
• 14.2 The Basis Set
• 14.3 The Extended Hückel Method
• 14.4 The Hartree-Fock Self-Consistent Field Approach
• 14.5 Density Functional Theory
• 14.6 Epilogue
• Problem

References for Further Reading

Answers to Selected Problems

• Chapter 1 Origins of Quantum Theory
• Chapter 2 Methods of Quantum Mechanics
• Chapter 3 Particles in Boxes
• Chapter 4 The Hydrogen Atom
• Chapter 5 Structure and Properties of More Complex Atoms
• Chapter 6 Vibrations and the Harmonic Oscillator
• Chapter 7 Molecular Rotation and Spectroscopy
• Chapter 8 Bonding and Properties of Diatomic Molecules
• Chapter 9 Hückel Molecular Orbital Calculations
• Chapter 10 Molecular Structure and Symmetry
• Chapter 11 Molecular Spectroscopy
• Chapter 12 Molecular Spectroscopy
• Chapter 13 Barrier Penetration