The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical model of physical objects is proposed. This model gives a possibility to unite a description of corpuscular and wave properties of real physical objects, i.e. fields and particles. There are substantiated an approach and a mathematical pattern which give a possibility to describe physical object not only in causal, but also in absolute remote fields of the Minkowski space. Applying the proposed approach to the microcosm description, one can get the equations that in passage to the limit transfer to such quantum mechanics equations as Schrodinger, Klein-Gordon-Fock and in particular case - the wave equation. The event nature of the received equations is discussed. It is shown that all mentioned equations reflect the space-time relativistic properties during the description of the invariant and non-invariant physics object characteristics.
We show that QM can be represented as a natural projection of a classical statistical model on the phase space Ω=H×H, where H is the real Hilbert space. Statistical states are given by Gaussian measures on Ω having zero mean value and dispersion of the Planck magnitude -- fluctuations of the ``vacuum field.'' Physical variables (e.g., energy) are given by maps f:Ω→R (functions of classical fields). The crucial point is that statistical states and variables are symplectically invariant. The conventional quantum representation of our prequantum classical statistical model is constructed on the basis of the Teylor expansion (up to the terms of the second order at the vacuum field point ω=0) of variables f:Ω→R with respect to the small parameter κ=h. A Gaussian symplectically invariant measure (statistical state) is represented by its covariation operator (von Neumann statistical operator). A symplectically invariant smooth function (variable) is represented by its second derivative at the vacuum field point ω=0. From the statistical viewpoint QM is a statistical approximation of the prequantum classical statistical field theory (PCSFT). Such an approximation is obtained through neglecting by statistical fluctuations of the magnitude o(h),h→0, in averages of physical variables. Equations of Schrödinger, Heisenberg and von Neumann are images of dynamics on Ω with a symplectically invariant Hamilton function.