One-dimensional scattering of a particle or a wave packet by a finite number of periodic potential barriers is studied. The fundamental physical mechanism that determines the transmission coefficient is shown to be quantum interference between waves with different numbers of inner reflections. The tendency of the transmission coefficient to saturate with respect to an increase in the number of barriers is due to the free-particle nature of a particle subject to a completely periodic potential.

The spreading of a free wave packet and its relation to classical and quantum dynamics are examined. The phase-space formulation using the Wigner distribution function provides a convenient representation in which each phase point of the distribution follows a classical trajectory and the spreading occurs as a result of classical dynamics. A different formulation using a different phase-space distribution function, however, does not allow this simple interpretation of the spreading.