Dynamical diffusion as the approximation of one quantum particle dynamics

The paper contains the proof that the diffusion ensemble of point wise particles with the intensity depending on the grain of spatial resolution serves as the satisfactory approximation of one quantum particle dynamics. The work continues the algorithmic approach to quantum mechanics that has been initiated in the works [4], [3]. The main aim of algorithmic approach is to build the video film reflecting the dynamics of many quantum particles. We believe that the modern computers make possible to create such video films that reflect the dynamics of billions quantum particles including all known quantum effects. Such video films must show all details of process that could be obtained by any sequence of observation fulfilled on the considered system. The creation of such picture we call the simulation of quantum dynamics. The simulation can be based on quantum theory only, because it is the single theory of micro world. At the same time the simulation of quantum dynamics represents the serious difficulty due to the fundamental difficulty of quantum computations. This difficulty lies in the formalism of quantum theory: the dimensionality of the space of states grows exponentially when the total number of particles grows. Though, the computational difficulties arise already for one quantum particle. Let its configuration space be divided to N elements. It means that the space of quantum states