New about the wave function,"Einstein's boxes'' and scattering a particle on a one-dimensional $\delta$-potential

TL;DR

This paper explores the relationship between the scattering of a particle on a one-dimensional delta potential and Einstein's boxes thought experiment, challenging traditional views on quantum state measurement and emphasizing the physical significance of the wave function's phase.

Contribution

It demonstrates the limitations of the superposition principle in these contexts and argues that the wave function's phase has a direct physical meaning, impacting measurement interpretations.

Findings

Superposition principle limitations in delta potential scattering and Einstein's boxes.

Wave function phase encodes physical information beyond statistical restrictions.

Quantum mechanics allows for simultaneous measurement of position and momentum at a point.

Abstract

The connection between the problem of scattering a particle on a one-dimensional $\delta$-potential with the "Einstein's boxes" thought experiment is shown. In both cases, the validity of the superposition principle is limited by Einstein's 'separation principle'. 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. First, even the square of the modulus of the wave function imposes more than just statistical restrictions. Second, the phase of the wave function also has a physical meaning -- it sets the field of pulses of the ensemble. That is, quantum mechanics not only does not prohibit the simultaneous measurement of the coordinate and momentum of a particle, but also predicts the value of the momentum at that spatial point where the particle will (accidentally) be detected.