Generalized Gaussian wave packet dynamics

We propose an extension of the semiclassical Gaussian wave packet dynamics to eliminate the three main restrictions of this method. The first restriction is that the wave packet is forced to remain Gaussian. This is correct only for quadratic, linear, or constant potentials. The second restriction is that the method is, in general, not able to treat most classically forbidden processes. The third restriction is that the norm is conserved only for Gaussian wave packets. For a superposition of Gaussians this is no longer true. We can eliminate these restrictions by an extension of the method into complex phase space, keeping time real.