Quantum Mechanics: Linear Algebra and Wave Mechanics

This lecture covers the link between linear algebra and wave mechanics, focusing on the operators defined in wave mechanics, such as the position and momentum operators, and their self-adjoint nature. It also explores the nearly free electron model as a perturbation problem in a periodic potential, leading to the splitting of energy levels at the Brillouin Zone. The lecture delves into the application of important linear algebra concepts to demonstrate the Bloch theorem and define the Brillouin Zone. Additionally, it introduces a probabilistic approach to diffusion in Quantum Mechanics, emphasizing the concepts of probability in QM and the probabilistic nature of atomic diffusion.