Plancherel's Identity and Schrödinger Equation

This lecture covers Plancherel's identity for Schwartz functions and the solution of the free Schrödinger equation with initial data in Schwartz space. It discusses the existence and uniqueness of the solution, smoothness in time, conservation of L^2 norm, and the explicit solution formula with a complex Gaussian kernel. The interpretation includes wave packet spreading and the particle escaping to infinity.