Steiljes electrostatic model with imaginary charges resolves wave-particle duality

TL;DR

This paper demonstrates that quantum bound states can be modeled as point vortices with imaginary charges, and under certain conditions, these vortices exhibit wave-like behavior, providing insights into wave-particle duality.

Contribution

It introduces a novel mapping of quantum bound states to point vortices with imaginary charges using the Steiljes electrostatic model, linking quantum states to classical vortex dynamics.

Findings

Quantum bound states correspond to point vortices with imaginary charges.

Vortices in a background field exhibit wave solutions under paraxial approximation.

Supports wave-particle duality through vortex model representation.

Abstract

In this paper, we show that the quantum bound state problems are mapped to $N$ point vortices with the identical circulation or strength using the Steiljes electrostatic model with imaginary charges. We also show that these $N$ point charges or vortices, become imaginary, in a constant background field will admit a wave solution under paraxial wave approximation. Therefore, in quantum mechanics as long as paraxial approximation is valid it behaves like a wave.