  We study neutrino oscillations in space within a realistic model in which
both the source and the target are considered to be stationary having
Gaussian-form localizations. The model admits an exact analytic solution in
field theory which may be expressed in terms of complementary error functions,
thereby allowing for a quantitative discussion of quantum-mechanical (coherent)
versus statistical (incoherent) uncertainties. The solvable model provides an
insightful framework in addressing questions related to propagation and
oscillation of neutrinos that may not be attainable by the existing approaches.
We find a novel form of plane-wave behaviour of neutrino oscillations if the
localization spread of the source and target states due to quantum mechanics is
of macroscopic size but much smaller than neutrinos' oscillation length.
Finally, we discuss the limits on the coherence length of neutrino oscillations
and find that they mainly arise from uncertainties of statistical origin.
