Probabilistic vs optical interpretation of quantum mechanics

TL;DR

This paper explores the differences and connections between probabilistic and optical interpretations of quantum mechanics, focusing on electromagnetic and Schrödinger fields, eigenvalue multiplicities, and topological patterns in quantum states.

Contribution

It demonstrates the link between electromagnetic fields and Schrödinger eigenfunctions, revealing how eigenvalue multiplicities relate to topological patterns and interpretations of quantum mechanics.

Findings

Electromagnetic and Schrödinger fields are mathematically connected.

Eigenvalue multiplicities enable complex topological patterns in quantum states.

Quantum and topological entanglements are shown to be equivalent under certain conditions.

Abstract

Although electrons and photons produce the same interference patterns in the two-slit experiments, the description of these patters is markedly different. This difference was analyzed by Bohm. Later on Sanz and Miret-Artes and others were able to squeeze the differences to zero. Fortunately, they left some room for developments presented in this Letter. We noticed that in the absence of sources the electromagnetic field can be represented by the complex scalar field. It is demonstrated that the same fields are being used in the non relativistic Schr\"odinger equation. The connection between the electromagnetic and Schr\"odinger fields allows to study the topology of zero sets (Chladni patterns) of Schr\"odinger eigenfunctions. The existence of these patterns is contingent upon the existence of eigenvalues of multiplicity higher than one. This is permissible only in Schr\"odinger's version of quantum mechanics. Presence of multiplicities is making quantum mechanical and topological entanglements equivalent.