Scattering from the Potential Barrier V=cosh^{-2} ωx from the Path Integration over SO(1,2)

Details Scattering from the Potential Barrier V=cosh^{-2} ωx from the Path Integration over SO(1,2) Scattering from the Potential Barrier V=cosh^{-2} ωx from the Path Integration over SO(1,2)

1996-09-23

arxiv.org/abs/hep-th/9609177v2

J.Phys.A30:173-184,1997

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1088/0305-4470/30/1/012

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.

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