Quantum Mechanics: Wave-Particle Duality of Electrons

This lecture discusses the wave-particle duality of electrons, illustrating how quantum mechanics describes particles as both waves and particles. The instructor explains the interactions of electrons with matter, emphasizing their behavior as wave functions characterized by frequency and wave vector. The lecture covers the principles of energy and momentum in quantum mechanics, introducing key relationships such as Planck's relation and the de Broglie hypothesis. The propagation of particles in a vacuum is analyzed, highlighting the concept of wave packets and their oscillatory modes. The instructor demonstrates how to describe wave functions using Fourier transforms and discusses the implications of measuring particle probabilities. The lecture also explores the significance of electron behavior in electron microscopes, detailing how high-energy electrons can achieve high resolution. Finally, the instructor presents simulations to illustrate the propagation of electrons and the differences between phase velocity and group velocity, reinforcing the importance of understanding electron behavior in quantum mechanics.