On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

Abstract

We consider a three-body one-dimensional Schrödinger operator with zero range potentials, which models a positive impurity with charge $\kappa >0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like ${\kappa }^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states.

References in corpus (2)

• Self-adjoint extensions of Coulomb systems in 1,2 and 3 dimensions
• H2 molecule in strong magnetic fields

Cited by in corpus (1)

• Asymptotics of the bound state induced by $\delta$-interaction supported on a weakly deformed plane