In this paper we discuss a solution of the free particle Schru007fodinger 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.
