We consider central-potential scattering and determine a path-integral representation for the $S$ matrix in polar coordinates. This is obtained by transforming to polar coordinates a Cartesian form of the nonrelativistic $S$ matrix given by Campbell et al., and implementing an idea of Faddeev to obtain the appropriate asymptotic conditions. Our results are applied to scattering in an inverse-square potential to determine the correct phase shifts as well as the $S$ matrix.We consider central-potential scattering and determine a path-integral representation for the $S$ matrix in polar coordinates. This is obtained by transforming to polar coordinates a Cartesian form of the nonrelativistic $S$ matrix given by Campbell et al., and implementing an idea of Faddeev to obtain the appropriate asymptotic conditions. Our results are applied to scattering in an inverse-square potential to determine the correct phase shifts as well as the $S$ matrix.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMay 15, 198011 citations

The Feynman Path Integral in Potential Scattering

Lecture notes in mathematicsJan 1, 20080 citations

We consider central-potential scattering and determine a path-integral representation for the

S

matrix in polar coordinates. This is obtained by transforming to polar coordinates a Cartesian form of the nonrelativistic

S

matrix given by Campbell et al., and implementing an idea of Faddeev to obtain the appropriate asymptotic conditions. Our results are applied to scattering in an inverse-square potential to determine the correct phase shifts as well as the

S

matrix.