  In this paper we discuss a solution of the free particle Schrodinger
equation in which the time and space dependence are not separable. The
wavefunction is written as a product of exponential terms, Hermite polynomials
and a phase. The peaks in the wavefunction decelerate and then accelerate
around t = 0. We analyse this behaviour within both a quantum and a
semi-classical regime. We show that the acceleration does not represent true
acceleration of the particle but can be related to the envelope function of the
allowed classical paths. Comparison with other "accelerating" wavefunctions is
also made. The analysis provides considerable insight into the meaning of the
quantum wavefunction.
