Part I A Brief Review of Classical and Quantum Mechanics

• Lagrangian and Hamiltonian formulation of Classical Mechanics
  
• Superposition principle and Hilbert spaces
  
• Canonical Quantization
  
• Review of time-independent and time-dependent perturbation theory
  
• The Periodic Table, molecules and bonds in a nutshell
  

Part II Crystals and Electronic Properties of Solids

• Crystals: Lattices, structure, symmetry, reciprocal lattice
  
• The electronic structure of crystals
  
• Single-electron dynamics: Acceleration theorems, Landau levels, Stark-ladder quantization
  

Part III Second Quantization and Elementary Excitations in Solids

• Lagrangian and Hamiltonian formulation of classical fields
  
• Canonical Quantization of fields ('Second Quantization')
  
• An example: Quantization of the Schrödinger Field
  
• Elements of Quantum Statistical Mechanics and the Spin-Statistics Theorem
  
• Quantization of the charge density: Plasmons
  
• Quantization of the vibrational properties of solids: Phonons
  
• Quantization of the Electromagnetic Fields: Photons
  
• Dielectric properties of semiconductors
  

Part IV Electron Scattering in Solids

• Generalities about scattering in semiconductors
  
• Electron-phonon Interactions
  
• Scattering with Ionized Impurities: Brooks-Herring and Conwell-Weisskopf models, Ridley's statistical screening, Friedel sum rule and partial-waves
  
• Coulomb interactions among free carriers, impact-ionization, Auger recombination
  
• Interfacial and line-edge roughness with examples: Si/SiO2, heterostructures, graphene nanoribbons
  
• Interfacial excitations with examples: III-Vs plasmon/phonon coupled modes, suspended grapheme
  
• Radiative Processes: The dipole approximation, absorption spectrum for III-Vs
  

Part V Electronic Transport

• The Density Matrix and the Liouville-von Neumann equation
  
• Overview of quantum-transport formalisms
  
• From Liouville-von Neumann to Boltzmann: The semiclassical limit.
  
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