Dangling bonds on CNT (Carbon NanoTube) surface induce the spurious surface states. These dangling bonds can be bonded by incoming nano particles which is associated wave function with different characters (localization at the surface) in respect to real quantized states. When the translational symmetry is broken, we can limit the calculation to an area like a ring or a super cell. This can be achieved by several theoretical methods. The most widely used theoretical tools to deal with nano structures are based on the envelope function. The envelope of the nano structure wave function is relied on several approximations which have been widely debated in the literature. These approaches have experienced a great success mainly due to a fair compromise between simplicity of the method and reliability of the results. By applying the Bloch theorem for CNT structure and defining the periodic boundary conditions, we can find a newly defined envelop wave function for nano particles in CNT structure by making two approximations, namely by smooth variation of the perturbation potential and the effective mass approximation. For this purpose, we need to consider appropriate boundary conditions in order to allow such flux of particles. The obtained results show that the equation fulfills all wave vectors and how nano particles perturb CNT structure.
Key words: Thin films, carbon nano tube, nano particles, envelop wave function.
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