Infrared Active Spectroscopy of Carbon Nanotubes: A Lie Algebraic Study

Abstract

Using the Lie algebraic method, the normal stretching modes of vibration of carbon nanotubes are calculated in the one-dimensional U(2) framework. Constructing the local Hamiltonian by invariant Casimir and Majorana operators in the same framework, we calculated the IR active vibrational energy levels of the carbon nanotubes, which agree with the experimental observations.

Keywords:

• Vibrational spectra
• Lie algebra
• Hamiltonian
• matrix operators
• carbon nanotubes