  We introduce an approximation scheme to perform an analytic study of the
oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian
wave packets, we show that the oscillation is bounded by a time-dependent
vanishing function which characterizes the slippage between the mass-eigenstate
wave packets. We also demonstrate that the wave packet spreading represents a
secondary effect which plays a significant role only in the non-relativistic
limit. In our analysis, we note the presence of a new time-dependent phase and
calculate how this additional term modifies the oscillating character of the
flavor conversion formula. Finally, by considering Box and Sine wave packets we
study how the choice of different functions to describe the particle
localization changes the oscillation probability.
