Calculus of Variations: Ground States in Quantum Mechanics

This lecture covers topics related to the Calculus of Variations, focusing on finding ground states in quantum mechanics by minimizing energy. It discusses the Euler Lagrange equation, Lagrange multipliers, and the stationary Schrödinger equation. The lecture introduces an abstract tool by Laurence Young and explores weak convergence of functions. It emphasizes the need for functions to be uniformly bounded and equi-integrable to approximate step functions. The lecture concludes with the Fundamental Theorem of Young Measure Theory.