  We have reexamined the problem of $n-\bar n$ oscillations for ultra-cold
neutrons (UCN) confined within a trap. It is shown that for up to $10^3$
collisions with the walls the process can be described in terms of wave
packets. The exact equation is derived describing the time-evolution of the
$\bar n$-component for an arbitrary number of collisions with the trap walls.
The $\bar n$-component grows linearly with time with enhancement factor
depending on the reflection properties of the walls.
