Elements of Quantum Theory of Solids

This course unit consists of two parts. The first part focuses more specifically on Dirac formalism in quantum mechanics, with illustrations in the case of the 1D harmonic oscillator and angular momentum, particularly for spin. The second part is an introduction to the use of quantum mechanics in the field of solid-state physics through its application to semiconductors.

Upon completion of this course unit, students will be able to:

• Using Dirac formalism to solve quantum mechanics problems
• Explain the characteristics of a 1D harmonic oscillator in quantum mechanics.
• Determine the properties associated with angular momentum and, in particular, spin.
• Apply quantum mechanics to the study of the properties of certain models of solid-state physics (metals in the free electron model, etc.).
• Explain the appearance of a band gap in crystalline semiconductors and the distinction between metals, semiconductors, and insulators.

Introduction to Quantum Physics

CCI

• Quantum mechanics in Dirac formalism
  • State space - Dirac notation
  • Postulates of Quantum Mechanics
  • X and P representation - link to Schrödinger formalism
  • Complete Sets of Commuting Observables
• 1D Harmonic Oscillator (Dirac formalism)
• Kinetic Momentum in Quantum Mechanics
  • Orbital angular momentum
  • Spin
• Covalent bond
• Metal: free electron model
• Periodic structures
  • Crystal symmetry
  • Reciprocal lattice - Brillouin zone
• Energy bands
  • Bloch functions
  • Quasi-free electron model
  • Electrons in a periodic potential - general case
  • Filling in reports - Fermi-Dirac statistics
  • Filling the energy bands: Metal - Insulator - Semiconductor

CM: 27 hours

Tutorial: 27 hours