Quantum Mechanics: Electron Propagation and Measurement

This lecture delves into the principles of electron propagation and the mathematical framework of quantum mechanics. It begins with the fundamental concepts of wave packets and their propagation in optical systems. The instructor explains the general principle of calculating propagation, including determining global modes and their energies, projecting input modes, and propagating each mode with its proper frequency. The discussion extends to the influence of the envelope on optical bits and the propagation of electronic bits in Fourier space. The lecture also covers the dispersion relation in a vacuum, illustrating the relationship between energy and momentum for electrons. The instructor introduces quantum operators, their definitions, and their application in measuring physical quantities. The concept of wave function collapse during measurement is explained, emphasizing the probabilistic nature of quantum mechanics. The lecture concludes with exercises on the Schrödinger equation and quantum operators, reinforcing the theoretical concepts presented throughout the session.