Quantum mechanics as applied mathematical statistics

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schrödinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.