Multi-variate Bateman method for two-body scattering without partial-wave decomposition
Kuruoğlu, Z. C.
Journal of Mathematical Chemistry
1857 - 1869
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The use of Bateman method for solving the two-variable version of the two-body Lippmann-Schwinger equation without recourse to partial-wave decomposition is investigated. Bateman method is based on a special kind of interpolation of the momentum representation of the potential on a multi-variate grid. A suitable scheme for the generation of a multi-variate Cartesian grid is described. The method is tested on the Hartree potential for electron-hydrogen scattering in the static no-exchange approximation. Our results show that the Bateman method is capable of producing quite accurate solutions with relatively small number of grid points.
Degenerate-kernel methods for integral equations
Multi-variate interpolation and approximation
Quantum scattering theory