2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125150We analyse the low lying spectrum of a model of excitons in carbon nanotubes. Consider two particles with an attractive Coulomb self-interaction, placed on an infinitely long cylinder. If the cylinder radius becomes small, the low lying spectrum is well described by a one-dimensional effective Hamiltonian which is exactly solvable.final version, accepted for publication in Annales Henri PoincareMathematical PhysicsMesoscale and Nanoscale Physics81V99text