  In this paper we look at transmission through one-dimensional potential
barriers that are piece wise constant. The Transfer Matrix approach is adopted
and a new formula is derived for multiplying long matrix sequences that not
only leads to an elegant representation of the wave function, but also results
in much faster computation than earlier methods. The proposed method covers a
broad spectrum of potentials of which multi-barrier systems are special cases.
The paradigm is exemplified with a finite lattice of non-uniform rectangular
barriers - non-uniformity being crucial, as the uniform case has been solved
exactly by Griffiths and Steinke. For the non-uniform multi-barrier problem,
the intervening wells strongly influence the transmission probability.
Surprisingly, we find that the wells act 'individually', i.e. their influence
is only a function of their width and is independent of their exact 'location'
in a multi-barrier system. This leads to a startling observation, which we have
termed as the 'Alias Effect.' The exact solutions are supported with asymptotic
formulas.
