  Probabilistic description of results of measurements and its consequences for
understanding quantum mechanics are discussed. It is shown that the basic
mathematical structure of quantum mechanics like the probability amplitude,
Born rule, probability density current, commutation relations, momentum
operator, uncertainty relations, rules for including the scalar and vector
potentials and existence of antiparticles can be derived from the definition of
the mean values of the space coordinates and time. Equations of motion of
quantum mechanics, the Klein-Gordon equation, Schroedinger equation and Dirac
equation are obtained from requirement of the relativistic invariance of the
theory. Limit case of localized probability densities leads to the
Hamilton-Jacobi equation of classical mechanics. Many particle systems are also
discussed.
