The improved Hagedorn wavepacket method for semiclassical Schrödinger equation

The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation.In this paper,a new semi-discretization in space is obtained by wavepacket operator.In a sense,such semi-discretization is equivalent to the Hagedorn wavepacket method,but this discretization is more intuitive to show the advantages of wavepacket methods.Moreover,we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation.The improved algorithms are of the Gauss–Hermite spec-tral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation.And for the given accuracy,the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation.The superiority is shown by the error estimation and numerical experiments.