On the unique solutions manifold of the Laughlin problem

TL;DR

This paper investigates the unique solutions of the Laughlin problem, providing explicit solutions and analyzing their physical significance, which enhances understanding of the correlated motion of electrons in magnetic fields and the related new state of matter.

Contribution

It explicitly expresses solutions in elementary functions for the Laughlin problem and explores their physical implications, offering new insights into magnetic field values and electron correlations.

Findings

Existence of exact solutions for specific magnetic fields

Physical interpretation of special magnetic field values

Relevance to the understanding of new states of matter

Abstract

Solutions, exactly expressed in terms of elementary functions (unique Laughlin states), of the correlated motion problem for a pair of 2D-electrons in a constant and uniform magnetic field have been shown to exist for a certain relation between the magnetic field induction and the electron charge. Arguments that can help to understand the physical meaning of these remarkable magnetic field values have been provided. The special interest to this problem is justified by the importance of the new state of matter recently observed.