Elements of Quantum Solid-State Theory

This lecture consists of two parts. The first part focuses specifically on Dirac’s formalism in quantum mechanics, with examples involving the 1D harmonic oscillator and angular momentum, particularly spin. The second part is an introduction to the use of quantum mechanics in solid-state physics through its application to semiconductors.

By the end of this course unit, students will be able to:

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

Introduction to Quantum Physics

CCI

• Quantum Mechanics in the Dirac Formulation
  • State Space - Dirac Notation
  • Postulates of Quantum Mechanics
  • X and P Representations—Connection to Schrödinger's Formalism
  • Complete Sets of Observables That Commute
• 1D Harmonic Oscillator (Dirac formalism)
• Angular 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
  • Quasifree Electron Model
  • Electrons in a Periodic Potential—General Case
  • Filling States - Fermi-Dirac Statistics
  • Filling the Energy Bands: Metal - Insulator - Semiconductor

CM: 27 hours

TD: 27 hours