dorsal/arxiv
View SchemaComparison of numerical methods for the calculation of cold atom collisions
| Authors | G. H. Rawitscher, B. D. Esry, E. Tiesinga, J. P. Burke |
|---|---|
| Categories | |
| ArXiv ID | physics/9909005 |
| URL | https://arxiv.org/abs/physics/9909005 |
| DOI | 10.1063/1.480431 |
Abstract
Three different numerical techniques for solving a coupled channel Schroedinger equation are compared. This benchmark equation, which describes the collision between two ultracold atoms, consists of two channels, each containing the same diagonal Lennard-Jones potential, one of positive and the other of negative energy. The coupling potential is of an exponential form. The methods are i) a recently developed spectral type integral equation method based on Chebyshev expansions, ii) a finite element expansion, and iii) a combination of an improved Numerov finite difference method and a Gordon method. The computing time and the accuracy of the resulting phase shift is found to be comparable for methods i) and ii), achieving an accuracy of ten significant figures with a double precision calculation. Method iii) achieves seven significant figures. The scattering length and effective range are also obtained.
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"abstract": "Three different numerical techniques for solving a coupled channel\nSchroedinger equation are compared. This benchmark equation, which describes\nthe collision between two ultracold atoms, consists of two channels, each\ncontaining the same diagonal Lennard-Jones potential, one of positive and the\nother of negative energy. The coupling potential is of an exponential form. The\nmethods are i) a recently developed spectral type integral equation method\nbased on Chebyshev expansions, ii) a finite element expansion, and iii) a\ncombination of an improved Numerov finite difference method and a Gordon\nmethod. The computing time and the accuracy of the resulting phase shift is\nfound to be comparable for methods i) and ii), achieving an accuracy of ten\nsignificant figures with a double precision calculation. Method iii) achieves\nseven significant figures. The scattering length and effective range are also\nobtained.",
"arxiv_id": "physics/9909005",
"authors": [
"G. H. Rawitscher",
"B. D. Esry",
"E. Tiesinga",
"J. P. Burke"
],
"categories": [
"physics.atom-ph",
"physics.comp-ph"
],
"doi": "10.1063/1.480431",
"title": "Comparison of numerical methods for the calculation of cold atom collisions",
"url": "https://arxiv.org/abs/physics/9909005"
},
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