Quantum Interference as a Process of Accumulation of Single-Particle Arrivals

Single-particle interference experiments brought new arguments supporting objective reality of matter and photon waves, compatibility of particle and wave properties of quantons, the evidence of existence of particles trajectories during the accumulation of an interference pattern, and the necessity of completing quantum mechanics by the description of single events. By integrating the probability density of transverse momenta multiplied by the probability density of particle distribution at the slits over all transverse momenta and over all slit points, we have derived the expression for the probability density for the particle's arrival at time t to a point behind a grating. The agreement with usual probability density given by the modulus square of the wave function in coordinate representation is very good in the far field. In the near field the agreement is poor. This was demonstrated previously for gratings with a small number of slits, and is demonstrated in our paper for a many-slits grating, where the Talbot Laue effect exists. Further study of the form of particles' trajectories in the near field is necessary. In addition to obtaining agreement with the distribution after many events have been accumulated in the far field, with this approach one might also obtain a distribution of a smaller number of events. For that we do not integrate over all momenta and slit points at the grating, but over randomly chosen ones