Quantum Mechanics: Mathematical Framework

This lecture introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in the context of quantum mechanics, contrasting it with classical mechanics. It outlines the content of the upcoming units, focusing on the description of a free quantum particle using Fourier transform and the spectral theory of unbounded operators for quantum measurement and stationary states. The slides cover various topics such as course logistics, homework details, basic function spaces review, single particle description in R3, potential functions, Hamiltonian operator, system states, measurement outcomes, and the role of observables in quantum mechanics.