Elements of Quantum Solid Theory

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

Upon completion of this UE, 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 in particular with spin
• Apply quantum mechanics to the study of the properties of some 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
  • Postulates of Quantum Mechanics
  • X and P representation - link with Schrödinger formalism
  • Complete Sets of Observables that Switch
• 1D Harmonic Oscillator (Dirac formalism)
• Kinetic Moment in Quantum Mechanics
  • Orbital angular momentum
  • Spin
• Covalent bonding
• Metal: free electron model
• Periodic structures
  • Crystal symmetry
  • Reciprocal network - Brillouin zone
• Energy bands
  • Bloch's functions
  • Quasi-free electron model
  • Electrons in a periodic potential - general case
  • Filling of states - Fermi-Dirac statistics
  • Filling of energy bands: Metal - Insulator - Semiconductor

CM : 27 h

TD : 27 h