Fractional Quantization and Fractional Quantum Hall Effect

TL;DR

This paper proposes a novel fractional quantization scheme for two-dimensional electrons using boundary conditions on a multi-layered Riemann surface, presenting wave functions and energies for fractional quantum Hall states.

Contribution

It introduces a new fractional quantization method based on Riemann surface boundary conditions, advancing understanding of fractional quantum Hall effects.

Findings

Fractional angular momentum quantization achieved

Wave functions for incompressible quantum fluid states derived

Cohesive and excitation energies calculated

Abstract

A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave functions for the incompressible quantum fluid states are presented and the cohesive and the excitation energies are given.