New about the wave function, ”Einstein’s Boxes” and scattering a particle on a 1D short-range potential

I hope that these two new results presented inarXiv:1805.03952v12

will be interesting:

I have found that the process of scattering a particle on a one-dimensional delta-potential (and any other short-range potential) is closely related to the thought experiment “Einstein’s Boxes”. I presented a new view on this experiment. The main feature of this view is that this experiment is directed not only against the doctrine of incompleteness of quantum mechanics (as Einstein thought), but also against the superposition principle in those one-particle problems where “Einstein’s Boxes” arise. The scattering process under study belongs to this class of problems. In this case the quantum one-particle dynamics loses the uniqueness property in the limits t→∞ and, hence, ceases to be unitary. Thus, the formal Hamiltonian with the delta-potential (and with any other short-range potential) has no everywhere dense domain, in the Hilbert space, where it would be defined as a linear operator. This means that this scattering process is a “mixture” of two co-developing sub-processes – transmission and reflection. Because of the interference between them, both at the initial stage of scattering and at the very stage of scattering, only an indirect measurement of the physical quantities of each subprocess is possible. A model is presented to describe these sub-processes at all stages of scattering.

It is also shown that the generally accepted point of view, according to which “To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements”, is fundamentally wrong. I show that even the squared modulus of the wave function imposes more than just statistical restrictions on the state of a quantum ensemble (remind, within the incompleteness doctrine, quantum mechanics describes quantum ensembles). As regards the phase of the wave function, it has sets the momentum field of the quantum ensemble. That is, quantum mechanics not only does not prohibit the simultaneous measurement of the coordinate and momentum of a particle, but yet predicts the value of the momentum at that spatial point where the particle will (accidentally) be detected.

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