Abstract
Unitary irreducible representation of the group SO(1,2) is obtained in the mixed basis, i.e. between the compact and non-compact bases, and new addition theorems are derived which are required in path integral applications involving a positively signed potential. The Green function for the potential barrier 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 are also presented.