Semi-classical description of electrostatics and quantization of electric charge

TL;DR

This paper proposes a semi-classical electrostatic model explaining electric charge quantization and classical phenomena, linking boundary conditions to charge discretization and field behavior.

Contribution

It introduces a semi-classical framework that explains charge quantization and classical electrostatic effects through boundary conditions and wavefunction constraints.

Findings

Electric charge must be a rational multiple of elementary charge under certain conditions.

Classical electrostatic phenomena are consistent with the semi-classical model.

The model suggests modifications to Gauss's law and Poisson's equation for quantized fields.

Abstract

In this work, we present an explanation of the electric charge quantization based on a semi-classical model of electrostatic fields. We claim that in electrostatics, an electric charge must be equal to a rational multiple of the elementary charge of an electron. However, the charge is quantized if the system has certain boundary conditions that force the wavefunction representing an electric field to vanish at specific surfaces. Next, we develop the corresponding model for the electric displacement vector. It is demonstrated that a number of classical results, e.g. bending of field lines at the interface of two dielectric media, method of images, etc. are all consistent with the predictions of this model. We also present the possible form of Gauss's law or (Poisson's equation), to find the wavefunctions of the field from a source charge distribution, in this model.