Contents

• Short Historical Introduction
  • Atoms and Molecules as a Concept
    • Greek Philosophy
    • Chemistry
    • Thermodynamics, Statistical Mechanics
    • Opponents to Atoms and Molecules
  • Discovery of Atoms
    • `Splitting of the Atom'
  • Theory of Atoms: Quantum Mechanics
    • `Old Quantum Mechanics'
    • Modern Quantum Mechanics
  
  
• Some Revision, Fine-Structure of Atomic Spectra
  • Hydrogen Atom (non-relativistic)
    • Non-relativistic Single Particle Quantum Mechanics
    • Coulomb Potential
    • Orbital Angular Momentum
    • Radial Solutions
  • A `Mini-Molecule': Perturbation Theory vs Non-Perturbative Bonding
    • Example: Two-Level System
  • Hydrogen Atom: Fine Structure
    • Kinetic Energy and Darwin Term
    • Spin-Orbit Coupling
    • Perturbation Theory for Fine Structure
  
  
• Introduction into Many-Particle Systems
  • Indistinguishable Particles
    • Permutations
    • Basis vectors for Fermi and Bose systems
  • 2-Fermion Systems
    • Two Electrons
    • Properties of Spin-Singlets and Triplets
    • The Exchange Interaction
  • Two-electron Atoms and Ions
    • Perturbation theory in
  
  
• The Hartree-Fock Method
  • The Hartree Equations, Atoms, and the Periodic Table
    • Effective Average Potential
    • Angular Average, Shells, and Periodic Table
  • Hamiltonian for Fermions
    • Expectation value of
    • Expectation value of
  • Hartree-Fock Equations
    • The Variational Principle
    • The Variational Principle for Many-Electron Systems
    • Hartree-Fock Equations
  
  
• Molecules
  • Introduction
    • Model Hamiltonian
  • The Born-Oppenheimer Approximation
    • Derivation
    • Discussion of the Born-Oppenheimer Approximation
    • Adiabaticity and Geometric Phases
    • Breakdown of the Born-Oppenheimer Approximation
  • The Hydrogen Molecule Ion
    • Hamiltonian for
    • The Rayleigh-Ritz Variational Method
    • Bonding and Antibonding
  • Hartree-Fock for Molecules
    • Roothan Equations
  
  
• Time-Dependent Fields
  • Time-Dependence in Quantum Mechanics
    • Time-evolution with time-independent
    • Example: Two-Level System
  • Time-dependent Hamiltonians
    • Spin in Magnetic Field
    • Landau-Zener-Rosen problem
  • Time-Dependent Perturbation Theory
    • Model Hamiltonian
    • The Interaction Picture
    • First Order Perturbation Theory
    • Higher Order Perturbation Theory
    • States
  
  
• Interaction with Light
  • Electromagnetic Fields and Maxwells Equations
    • Longitudinal and transversal parts
    • Potentials
  • Gauge invariance in single-particle non-relativistic QM
    • Local Gauge Transformation
  • Gauge invariance for many charges in non-relativistic QM
    • Charge and current densities, polarization and magnetization
    • The Hamiltonian
    • Power-Zienau-Woolley Transformation
    • Some Remarks on Fields
  
  
• Rotations and Vibrations of Molecules
  • Vibrations and Rotations in Diatomic Molecules
    • Hamiltonian
    • Angular Momentum
    • Radial SE
    • Spin
    • Beyond the Harmonic Approximation
  • Selection Rules
    • Dipole Approximation
    • Pure Rotation
    • Pure Vibration
    • Vibration-Rotation Spectra
  • Electronic Transitions
    • The Franck-Condon Principle
  
  
• Interaction between Molecules
  • From microscopic to macroscopic
    • Introduction
    • General considerations
  • Effective Potentials
    • Electrostatics: multipole expansions
    • Effective Interaction between Molecules
    • First oder term: static dipole-dipole interaction
    • Second oder term: (London) dispersion forces (van-der-Waals forces)
  
  
• Examples
  • Two-Level System
    • .
  • Hydrogen Atom
    • .
    • .
  • Bosons and Fermions
    • .
    • .
    • .
    • .
  • Hartree-Fock
    • .
    • .
  • Molecules
    • .
    • .
  • Time-Dependence
    • .
    • .
  
  
• Bibliography
• Index
• About this document ...

©T. Brandes 2005