Elements of Quantum Solid Theory

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

On completion of this course, students will be able to :

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

Introduction to quantum physics

CCI

• Quantum mechanics in the Dirac formalism
  • State space - Dirac notation
  • Quantum mechanics postulates
  • X and P representation - link with Schrödinger formalism
  • Complete sets of Commutating Observables
• 1D harmonic oscillator (Dirac formalism)
• Kinetic Momentum in Quantum Mechanics
  • Orbital angular momentum
  • Spin
• Covalent bonding
• Metal: free electron model
• Periodic structures
  • Crystal symmetry
  • Reciprocal network - Brillouin zone
• Energy bands
  • Bloch functions
  • Quasi-free electron model
  • Electrons in a periodic potential - general case
  • State filling - Fermi-Dirac statistics
  • Filling of energy bands: Metal - Insulator - Semiconductor

CM: 27 h

TD: 27 h