"The acceleration effect in quantum mechanics"

Zakharov M.A.

The report is devoted to the development of ideas about the Acceleration Effect as a general physical effect formulated in the recent work of A. I. Frank. It is devoted to the presentation of the results of a numerical study of the manifestation of the acceleration effect in the interaction of a particle with various accelerating quantum objects.

A wave packet with parameters characteristic of ultracold neutrons was considered as a particle. Various planar potential structures were used as quantum objects, namely: potential step, potential barrier, potential well, double potential step, interference filter, two-layer structure.

The problems were studied by numerically solving the nonstationary Schrödinger equation by splitting the evolution operator. The spectra of the resulting state after the interaction of the packet with the object were obtained.

The results demonstrate a pronounced presence of the acceleration effect in all studied problems. In the case of resonant structures, the acceleration effect is proportional to the lifetime of the state inside the object (which can be many times longer than the time of flight of a particle). The results obtained confirm the hypothesis that the acceleration effect is a consequence not so much of the passage of a particle through an accelerated refractive sample, as the existence of a nonzero interaction time in quantum mechanics.

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