Time-dependent Hartree Approximation and Ehrenfest Dynamics

This lecture covers the principles of the time-dependent Hartree approximation (TDHA) and its application in the Toupe principle. It also discusses the mean-field and single-particle approximations, as well as the concept of gauge conditions and the initial conditions for the system. The lecture further explores the Ehrenfest dynamics, focusing on the mixed quantum-classical dynamics and the molecular time-dependent Schrödinger equation. Various alternative parametrizations and propositions related to the TDHA are presented, along with the concept of mean-field Hamiltonians and energy conservation. The lecture concludes with an examination of the Ehrenfest theorem and its implications in molecular dynamics.