  We analyse tunnelling of a single particle, whose initial state is given by a
superposition of spatially separated wave packet modes. It is shown that "pile
up" of different components the scatterer may change the tunnelling
probabilities, making such states a convenient tool for probing the barrier's
scattering times. Interference effects arising in resonance tunnelling in are
studied in detail. The analysis allows us to gain further insight into the
origin of interference effects in scattering of several identical particles.
