  Electron transmission and wave functions through junctions with a pair of a
pentagonal defect and a heptagonal defect connecting two metallic carbon
nanotubes are analyzed by the analytical calculation with the effective mass
equation. The energy region $|E| < E_c$ is considered where the channel number
is kept to two. Close relation between the transmission rate and the wave
function is found; the transmission rate is given by the inverse squared
absolute value of the wave function. The dependence of the transmission rates
on the energy and on the size of the junction is clearly explained by the
nature of the wave function. Though the wave function and the transmission rate
calculated by the tight binding model agree well with the corresponding
analytical results by the effective mass approximation, the discrepancy becomes
considerable when $|E| \simeq E_c$. To study the origin of this discrepancy, an
efficient numerical calculation method is developed with a generalized transfer
matrix for the tight binding model. Their numerical results are compared with
the corresponding analytical ones and the results show that the origin of the
discrepancy comes from the evanescent waves with the longest decay length in
the tube parts.
