On the critical dipole moment in one-dimension

TL;DR

This paper determines the minimum electric dipole strength required for a one-dimensional system to support bound states, providing insights into the conditions necessary for binding in dipolar quantum systems.

Contribution

It introduces a calculation of the critical dipole moment in 1D systems, a novel criterion for the existence of bound states in dipolar interactions.

Findings

Derived the critical dipole moment for bound state formation

Identified conditions under which 1D dipolar systems support bound states

Provided analytical expressions for the minimum dipole strength

Abstract

We calculate the minimum magnitude an electric dipole must have for a 1D system, interacting through the dipole, to support bound states.