The energy eigenvalues of the channeled electrons through single wall carbon nanotubes (n,m) was calculated.  According to the continuum model approximation given by Lindhard for the case of an axial channeling in single crystals, the actual periodic potential of a row of atoms is replaced by a potential averaged over a direction parallel to the row, called continuum potential. The calculations was executed by using the atomic interaction potential as given by Moliere potential. The maximum number of bound states and the energy eigenvalues is calculated for positrons of 100 MeV energy incident in a direction parallel to the nanotube axis, by using WKB method. The calculations showed that the effect of temperature by using Debye approximation of thermal vibration amplitude on the channeling potential is very small and gave the same eigenvalues and the same number of bound states as that for the static nanotubes.

Calculation of the number of bound states n for channeled electrons through single wall carbon nanotubes (n,m) at different values of electrons energy by using (Wetzel, Kramer's, Brillouin approximation)(WKB) method. The calculations executed according to the continuum model approximation given by Lindhard for the case was carried out of an axial channeling in single crystals. The estimated results of the maximum number of bound states of the channeled electrons in a zigzag (n, 0), armchair (n,n) and chiral(n,m) nanotubes have been performed using the Moliere potential. In this work we determined the emitted photon energy due to n, (n-1) transitions between higher -quantum states as a function of the electron energy up to 500 MeV. Also the energy levels of electrons channeled in different types of single wall carbon nanotubes by using Moliere potential were defined.It has been showed that the emitted photon energy in the forward direction is the energy difference between the successive initial and final states of the channeled electron. The energy of the emitted channeling radiation has been calculated for incident electron at 50 MeV. We calculated the emitted channeling radiation for incident electrons at 10, 50 and 500 MeV with frequency in X-ray range.

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