  Exactly solvable models are interesting for science and education, since they
help in scientific search and in understanding of phenomena. Some exact
solutions for simple quantum-mechanical models are considered. The models
include two barriers, combinations of barrier pairs, three barriers, three
wells etc. The model of two barriers can predict some interesting phenomena in
the one-dimensional case. Clearing of wave and quantum-mechanical barriers
(including reflection-free passage) is an important problem of physics. The
rigorous equations for the transmission and reflection coefficients are
derived. Barriers in substances are combined into associations, where the bond
within each association is stronger than bonds between associations. Some
properties of disordered media (the transparency of glasses, the conductivity
of alloys or melts, the brittleness, or ductility, etc.) can be qualitatively
understood from this viewpoint. The same material can exhibit various
properties: transparent and opaque, metallic and non-metallic, ordered and
disordered, and so on. Such transitions can occur under pressure. A model of
the three-well potential can be applied to the phenomena under consideration.
Some remarks on 3-D cases are made.
