Time-Dependent Schrödinger Equation: Basis Set Solutions

This lecture covers the basis set solutions of the time-dependent Schrödinger equation (TDSE) with a time-dependent Hamiltonian, focusing on the interaction with molecular systems and external fields. The instructor explains the process of solving the TDSE with the Hamiltonian operator, introducing an ansatz for the wavefunction and substitution into the TDSE. Special cases involving Gaussian wave packets, multiple-spawning, and coupled coherent states are also discussed.