2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174352Recent two-photon photo-luminescence experiments give accurate data for the ground and first excited excitonic energies at different nanotube radii. In this paper we compare the analytic approximations proved in \cite{CDR}, with a standard variational approach. We show an excellent agreement at sufficiently small radii.Accepted for publication in Contemporary MathematicsMathematical PhysicsMesoscale and Nanoscale Physicstext