Quantum Mechanics: Wave Functions and Operators

This lecture covers the fundamental concepts of quantum mechanics, focusing on wave functions and operators. It starts by explaining the Schrödinger equation and its solutions for free particles and potential wells. The Heisenberg commutation relation is introduced, leading to the Heisenberg uncertainty principle. The lecture also delves into the concept of stationary states and the Hamiltonian operator. Additionally, it discusses the quantification of energy and uncertainty in quantum measurements, emphasizing the importance of observable quantities and operators. The implications of the Heisenberg commutation relation on the order of operators' application are explored, along with the behavior of particles in potential wells with barriers.