Wave Mechanics as Realistic Local Theory without Hidden Variables and Measurement Problem

TL;DR

This paper identifies fundamental issues in wave mechanics, proposing a local theory that resolves the measurement problem and clarifies the interpretation of the wave function by reformulating the Schrödinger equation.

Contribution

It reveals shortcomings in standard wave mechanics, corrects the superposition principle, and reformulates the Schrödinger equation as local equations for momentum fields.

Findings

Superposition principle contradicts exact solutions in scattering problems.

Wave function's amplitude and phase determine local momentum fields.

Schrödinger equation can be expressed as local equations for these fields.

Abstract

Two essential shortcomings of the axiomatics of wave mechanics are revealed, which make its consistent interpretation impossible. The first is that the standard formulation of the superposition principle contradicts the exact solutions of the Schr\"{o}dinger equation in the problem of scattering a particle on a one-dimensional delta potentia. Thus, the theorem on the irreducibility of the Schr\"{o}dinger representation is erroneous, and the wave function describing the state of a particle as a closed system can be either pure or mixed. The second shortcoming is the incompleteness of the Born, statistical interpretation of the wave function describing the pure state. It is shown that its amplitude and phase uniquely determine two fields of the particle's momentum; the Schr\"{o}dinger equation can be written as a closed system of local equations for these fields.