Comparison of numerical methods for the calculation of cold atom collisions

Comparison between three different numerical techniques for solving a coupl ed channel Schrodinger equation is presented. The benchmark equation, which describes the collision between two ultracold atoms, consists of two chann els, each containing the same diagonal Lennard-Jones potential, one of posi tive and the other of negative energy. The coupling potential is of an expo nential form. The methods are (i) a recently developed spectral type integr al equation method based on Chebyshev expansions, (ii) a finite element exp ansion, and (iii) a combination of an improved Numerov finite difference me thod and a Gordon method. The computing time and the accuracy of the result ing phase shift is found to be comparable for methods (i) and (ii), achievi ng an accuracy of ten significant figures with a double precision calculati on. Method (iii) achieves seven significant figures. The scattering length and effective range are also obtained. (C) 1999 American Institute of Physi cs. [S0021-9606(99)01347-1].