Extended Gaussian wavepacket dynamics

We examine an extension to the theory of Gaussian wavepacket dynamics in a one-dimensional potential by means of a sequence of time-dependent displace ment and squeezing transformations. Exact expressions for the quantum dynam ics are found, and relationships are explored between the squeezed system, Gaussian wavepacket dynamics, the time-dependent harmonic oscillator, and w avepacket dynamics in a Gauss-Hermite basis. Expressions are given for the matrix elements of the potential in some simple cases. Several examples are given, including the propagation of a non-Gaussian initial state in a Mors e potential.