Scattering from the potential barrier V=cosh(-2)wx from the path integration over SO(1,2)

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 V = cosh(-2) omega 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(0)t) are also presented.