  We suggest a somewhat non-standard view on a set of curious, paradoxical from
the standpoint of simple classical physics and everyday experience phenomena.
There are the quantisation (discrete set of values) of the observables (e.g.,
energy, momentum, angular momentum); forbidden simultaneous measurements of the
observables in the most cases (e.g., of a coordinate and momentum, of angular
momentum projections on difference axis); counter-intuitive relations on the
simultaneously measurable quantities (e.g., the famous expression for the
square momentum $l(l+1)$ with the maximal projection $l$). These and other
paradoxes are traditionally related to "purely quantum" phenomenon, i.e.,
having no analogue in the "classical world" ones. However, there are deep
analogies between classical and "quantum" worlds, as soon as the quantum
technique is applied to the classical phenomenon. We follow these analogies
with the examples of relatively simple and well known models of classical
physics, such as a simplified model of light transition through the media, a
system of electric charges close to each other and far from the observer; the
specific of motion in the Coulomb/Newtonian field. This text can be considered
as a mini-course addressed to higher school and undergraduate students who are
interested in basics of quantum mechanics, but are not yet ready for systematic
study of standard courses. The text may be also useful to those who supervise
such students.
