  Unitary irreducible representation of the group SO(1,2) is obtained in the
mixed basis, i.e. between the compact and noncompact basis and the new addition
theorems are derived which are required in path integral applications involving
the positively signed potential. The Green function for the potential barrier
$V=cosh^{-2}\omega x$ is evaluated from the path integration over the coset
space SO(1,2)/K where K is the compact subgroup. The transition and the
reflection coefficients are given. Results for the moving barrier
$V=\cosh^{-2}\omega (x-g_0t)$ are also presented.
