コロキウム

I will talk about the Hamiltonian formulation of Gaussian wave packets as an approximation to expectation value dynamics of the semiclassical Schr\"odinger equation with a Gaussian as the initial condition. Specifically, we formulate the Hamiltonian dynamics of the Gaussian wave packet using the symplectic structures behind the Schr\"odinger equation and the Siegel upper half space. It results in a correction term to the conventional formulation using the classical Hamiltonian system by Hagedorn and others. The main result is a proof that our formulation gives, under certain conditions on the potential function, a higher-order approximation than the classical formulation does to the dynamics of the expectation values of the position and momentum.