  The probability density distributions for the ground states of certain model
systems in quantum mechanics and for their classical counterparts are
considered. It is shown, that classical distributions are remarkably improved
by incorporating into them the Heisenberg uncertainty relation between position
and momentum. Even the crude form of this incorporation makes the agreement
between classical and quantum distributions unexpectedly good, except for the
small area, where classical momenta are large. It is demonstrated that the
slight improvement of this form, makes the classical distribution very similar
to the quantum one in the whole space. The obtained results are much better
than those from the WKB method. The paper is devoted to ground states, but the
method applies to excited states too.
