Fundamentals of Quantum Mechanics

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

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

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

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

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

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

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

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

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

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

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

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

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

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