Premium
Multiple surface molecular motion: A t ‐matrix approach
Author(s) -
Linderberg Jan
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560200861
Subject(s) - fredholm integral equation , integral equation , saddle point , scattering , separable space , mathematical analysis , matrix (chemical analysis) , scattering theory , mathematics , residual , equations of motion , surface (topology) , s matrix , rank (graph theory) , function (biology) , physics , quantum mechanics , chemistry , geometry , chromatography , algorithm , combinatorics , evolutionary biology , biology
Sets of coupled differential equations encountered in quantum mechanical scattering theory are converted to integral equations by means of a Wentzel‐Kramers‐Brillouin type Green's function. The residual terms are analyzed and it is shown that the resulting set of integral equations may be well approximated by a low order Fredholm expansion. The saddle point method for the approximate evaluation of integrals is seen to be equivalent to a replacement of the residual terms with a separable potential of low rank. Applications to scattering problems and chemical reactions are pointed out.