Variational Principle in Quantum Mechanics

This lecture introduces the variational principle in quantum mechanics, focusing on optimizing trial wave functions to approximate the ground state energy. The discussion covers the Hamiltonian operator, ground state energy, variational optimization, and Monte Carlo methods. The lecture also explores the application of deep neural networks in solving the Schrodinger equation for complex systems, emphasizing the importance of smart preprocessing and the use of known theory to fix network parameters. The presentation includes a detailed analysis of the electronic cost function, Hartree-Fock method, Slater determinants, and the impact of multi-determinants and backflow functions on computational accuracy. The lecture concludes with a discussion on the efficient computation of large molecules using neural networks and the significance of incorporating physical knowledge into machine learning models.