We examine an extension to the theory of Gaussian wave packet dynamics in a
one-dimensional potential by means of a sequence of time dependent displacement
and squeezing transformations. Exact expressions for the quantum dynamics are
found, and relationships are explored between the squeezed system, Gaussian
wave packet dynamics, the time dependent harmonic oscillator, and wave packet
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 Morse potential