Rigorous perturbation theory versus variational methods in the spectral study of carbon nanotubes

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Recent 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 Mathematics

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