  Two rectangular models described by the one-dimensional Schroedinger equation
with sharply localized potentials are suggested. The potentials have a
multi-layer thin structure being composed from adjacent barriers and wells.
Their peculiar tunneling properties are studied in considerable detail.
Particularly, in the zero-range limit when the potentials are squeezed to a
single point, sharp peaks with total transmission are observed at certain
(positive and negative) quantized values of the potential strength constant
forming infinite discrete sets. Beyond these sets, the barrier-well structures
behave as a perfectly reflecting wall. The transcendental equations with
respect to potential strengths, the solutions of which determine transmission
(resonance) sets, are derived. In this regard, both the models are exactly
solvable. The energy dependence of an incident particle is shown to reveal a
resonance behavior, being completely different from that observed in a typical
double barrier structure.
