Quantum Mechanics: Schrödinger Equation

This lecture covers the Schrödinger equation in quantum mechanics, the semi-implicit Crank-Nicolson scheme, quantum mechanical observables, and the free particle with wave packet spreading. It also discusses unitarity, temporal discretization, and the properties of the propagator. The lecture delves into the application of the exponential operator, the conservation of probability, and the properties of Hermitian operators. It explores the average energy conservation, probabilistic interpretations, and the spread of wave packets. The lecture concludes with discussions on spatial discretization, linear algebraic systems, and the effects of dispersion and diffusion.