Approximation of semiclassical expectation values by symplectic Gaussian wave packet dynamics

This paper concerns an approximation of the expectation values position and momentum solution to semiclassical Schrödinger equation with a Gaussian as initial condition. Of particular interest is obtained by our symplectic/Hamiltonian formulation wave packet dynamics that introduces correction term conventional using classical Hamiltonian system Hagedorn others. The main result proof gives higher-order than does value under certain conditions on potential function. Specifically, parameter $$\varepsilon $$ approaches 0, $$O(\varepsilon ^{3/2})$$ dynamics, whereas one )$$ approximation.