The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(ωx)$ is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for this potential into a path integral for the Morse potential problem. The dimensional extension technique is seen to be essential for performing the multiple integral representation of the propagator. The correctly normalized scattering wave functions and the scattering function are derived. To test the method employed, the free particle and the $δ-$ function barrier are considered as limiting cases.The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(ωx)$ is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for this potential into a path integral for the Morse potential problem. The dimensional extension technique is seen to be essential for performing the multiple integral representation of the propagator. The correctly normalized scattering wave functions and the scattering function are derived. To test the method employed, the free particle and the $δ-$function barrier are considered as limiting cases.

arXiv:quant-ph/0302009NCimBFeb 2, 20030 citations

The Feynman Path Integral in Potential Scattering

Lecture notes in mathematicsJan 1, 20080 citations

Test of a path-integral approach for the computation of scattering cross sections on an exactly solvable model

Valery V Smirnov

A numerical approach in scattering theory based on the path-integration technique is considered. An evaluation of a discretized Feynman path integral with an accurate Gaussian expansion of the integrand was used for the calculation of the differential cross sections for the scattering of a wave packet by a three-dimensional spherically symmetric Gaussian potential. The results are compared with the precise calculations using the phase functions method. This reveals separately discretization errors of the path integral, which depends on the single parameter---the number of discrete path points. High accuracy of the approach is demonstrated.A numerical approach in scattering theory based on the path-integration technique is considered. An evaluation of a discretized Feynman path integral with an accurate Gaussian expansion of the integrand was used for the calculation of the differential cross sections for the scattering of a wave packet by a three-dimensional spherically symmetric Gaussian potential. The results are compared with the precise calculations using the phase functions method. This reveals separately discretization errors of the path integral, which depends on the single parameter---the number of discrete path points. High accuracy of the approach is demonstrated.

Physical Review ANov 13, 20078 citations

The Feynman path integral in potential scattering

Sergio A Albeverio, Raphael J. Høegh-Krohn

Lecture notes in mathematicsJan 1, 19760 citations

On the path integration for the potential barrier

V_{0}\cosh ^{-2}(ωx)

The propagator associated to the potential barrier

V=V_{0}\cosh ^{-2}(ωx)

is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for this potential into a path integral for the Morse potential problem. The dimensional extension technique is seen to be essential for performing the multiple integral representation of the propagator. The correctly normalized scattering wave functions and the scattering function are derived. To test the method employed, the free particle and the

δ-

function barrier are considered as limiting cases.