Introduction to the Quantum World of Atoms and Molecules

The following sections are included:

• Preface

• Contents

The following sections are included:

• Early Atomic Theories

• The Chemical Atom

• The Kinetic Molecule

• The Spectroscopic Atom

• Antiatomism

• The Discovery of the Electron. The Planetary Atom

• The Constituents of Atoms and Molecules. The Modern View

• External Interactions. Photons

• Supplementary Reading

• Problems

The following sections are included:

• Black-Body Radiation and Planck's Discovery

• Photons and the Photoelectric Effect

• The Photon is a Relativistic Particle

• The Heat-Capacity Problem

• Bohr's Theory of the Hydrogen Atom

• De Broglie Waves

• Supplementary Reading

• Problems

The following sections are included:

• The Time-Dependent Schrödinger Equation

• The Time-Independent Schrödinger Equation

• Schrödinger Operators

• The Statistical Interpretation

• Supplementary Reading

• Problems

The following sections are included:

• Introduction

• The One-Dimensional Box

• Orthogonality of Wavefunctions

• Number of Nodes Versus Energy

• Inversion Symmetry

• The Three-Dimensional Box

• The Concept of Degeneracy

• The Free-Electron Model

• Non-Stationary States

• Supplementary Reading

• Problems

The following sections are included:

• The Bra-Ket Notation

• Linear Operators. The Commutator

• Hermitian Operators. Hermitian Conjugation

• Some Properties of Hermitian Operators

• Expectation Values and Uncertainties

• The Particle in a Box Revisited

• Commuting Hermitian Operators

• The General Uncertainty Principle

• Quantum Theory and Measurements

• Matrix Algebra

• Supplementary Reading

• Problems

The following sections are included:

• The Stationary States of the Free Particle

• Non-Stationary States of the Free Particle

• The Gaussian Wave Packet

• From One to Three Dimensions

• Supplementary Reading

• Problems

The following sections are included:

• Definitions

• The Schrödinger Equation for the Harmonic Oscillator

• Solving the Schrödinger Equation

• The Wavefunctions

• The Algebraic Method

• Supplementary Reading

• Problems

The following sections are included:

• The Reduced Mass of a Two-Body System

• Spherical Polar Coordinates

• Spherical Harmonics
  • The Dimensionless Angular-Momentum Operators
  • Looking for Common Eigenfunctions of and
  • The Raising and Lowering Operators
  • The Quantum Number l
  • A Phase Convention
  • The Analytical Expressions

• The Radial Function P(r)

• Supplementary Reading

• Problems

The following sections are included:

• The Effective Potential. General Notation

• The Radial Equation for the Hydrogen-Like Atom

• The Normalized Radial Functions

• Radial Probability Densities

• The Complete Wavefunctions

• Supplementary Reading

• Problems

The following sections are included:

• General Angular Momentum Theory

• Spin, Spin Functions and Spin-Orbitals

• Properties of the Spin One-Half Operators

• The One-Electron Atom in External Fields
  • The Hamiltonian With Spin Neglected
  • The Hamiltonian With Spin Included
  • The Refined Hamiltonian

• The Zeeman Effect

• The Pauli Equation

• Angular-Momentum Theory and Rotations

• Supplementary Reading

• Problems

The following sections are included:

• The Many-Electron Atom

• Neglect of Electron-Electron Repulsion

• The Aufbau Principle

• Exchange Degeneracy

• Pauli's Exclusion Principle. Slater Determinants

• Including Electron-Electron Repulsion

• Slater Type Orbitals

• Supplementary Reading

• Problems

The following sections are included:

• Introduction

• Variational Principles

• The Time-Independent Schrödinger Equation

• The Variational Method

• The Linear Variational Method

• Factorization of Secular Problems

• Supplementary Reading

• Problems

The following sections are included:

• The Adiabatic Approximation

• One-Electron Diatomic Molecules

• The LCAO Approximation

• The Homonuclear Case. Ground State of

• LCAO-MOs for Homonuclear Diatomics

• Electronic Structure of Homonuclear Di-atomics

• Supplementary Reading

• Problems

The following sections are included:

• Introduction

• The Vibrational Motion

• The Vibrating Rotator

• On Rotational and Vibrational Spectra

• Supplementary Reading

• Problems

The following sections are included:

• Orthonormal Bases and Unitary Matrices

• Coupling of Two Angular Momenta
  • The Uncoupled Representation
  • The Coupled Representation

• Vector-Coupling Coefficients by the Construction Method
  • Coupling of Two Spin ½ Particles
  • Coupling of Spin and Orbital Angular Momentum

• Angular Momenta in Many-Electron Atoms
  • The Total Orbital Angular Momentum
  • The Total Spin Angular Momentum
  • L-S Coupling
  • Adding the Nuclear Angular Momentum. Bose–Einstein Condensates

• Supplementary Reading

• Problems

The following sections are included:

• Operating on Slater Determinants

• Term Wavefunctions
  • The Helium Atom
  • The Carbon Atom

• Matrix Elements Between Slater Determinants

• Energies of Atomic Terms
  • The Helium Atom
  • The Beryllium Atom
  • The Carbon Atom

• Hund's Rules

• Supplementary Reading

• Problems

The following sections are included:

• The Oxygen Molecule. Term Analysis

• The Oxygen Molecule. Real Wavefunctions

• The Oxygen Molecule. Term Energies

• Supplementary Reading

The following sections are included:

• Hartree–Fock Method for a Single Determinant

• Spin Restrictions

• Conventional Hartree–Fock Theory

• The Correlation Problem

• Supplementary Reading

The following sections are included:

• Reduced Density Matrices

• Single Slater Determinant

• The Hohenberg-Kohn Theorem

• The Kohn–Sham Equations

• Supplementary Reading