  A quantum expansion parameter, analogous to the Hubble parameter in
cosmology, is defined for a free particle quantum wavefunction. By considering
the universe as an initial single Gaussian quantum wavepacket whose mass is
that of present-day observable universe and whose size is that of the Planck
Length at the Planck Time, it is demonstrated that this quantum expansion
parameter has a value at the present epoch of the same order as the value of
the Hubble constant. The coincidence suggests examining the effect of including
this type of quantum wave expansion in traditional general relativistic
cosmology and a sample model illustrating this is presented here. Using
standard Einstein-de Sitter cosmology ($\Omega$m = 1) it is found that cosmic
acceleration (aka dark energy) arises naturally during cosmic history. The time
at which the universe switched from deceleration to acceleration
(observationally ~7 Gyr before the present epoch) yields a value for the mass
of the wavepacket representing the universe at the Planck Time and its present
age. This same mass may then be used to obtain a curve for the cosmic expansion
rate versus z. This curve is well fit to observational data. The model is used
also to obtain an estimate of the inflationary expansion factor.
