Theoretical basis for the unification of the integer and the fractional quantum Hall effects

TL;DR

This paper develops a theoretical framework that unifies the integer and fractional quantum Hall effects by analyzing electron wave functions and densities without relying on fractional charge concepts.

Contribution

It provides a novel theoretical basis for unifying the integer and fractional quantum Hall effects through wave function analysis and electron density calculations.

Findings

Unified explanation of quantum Hall effects without fractional charge

Derived electron density and motion area in magnetic fields

Supports a common theoretical foundation for both effects

Abstract

This paper intends to provide a theoretical basis for the unification of the integer and the fractional quantum Hall effects. Guided by concepts and theories of quantum mechanics and with the solution of the Pauli equation in a magnetic field under the symmetric gauge, wave functions, energy levels of single electrons, and the expectation value of electron's spatial scope are presented. After the quotation of non-interaction dilute gas system, the product of single electron's wave functions is used to construct wave functions of the N electron gas system in magnetic field. Then the expectation value of the system's motion area and the electron's surface density are obtained. In this way, the unification explaination of the integer and the fractional quantum Hall effects is formulated without the help of the concept of fractional charge.