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arXiv physics/9909005physics.atom-phphysics.comp-ph
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冷原子碰撞计算的数值方法比较

Comparison of numerical methods for the calculation of cold atom collisions

G. H. Rawitscher, B. D. Esry, E. Tiesinga, J. P. Burke

摘要:

比较了三种不同的数值方法求解耦合通道薛定谔方程。该基准方程描述了两个超冷原子之间的碰撞,由两个通道组成,每个通道包含相同的对角Lennard-Jones势,一个具有正能量,另一个具有负能量。耦合势为指数形式。这些方法是i)最近发展的基于Chebyshev展开的谱型积分方程方法,ii)有限元展开,以及iii)改进的Numerov有限差分方法和Gordon方法的组合。发现对于方法i)和ii),计算时间和所得相移的准确度是相当的,在双精度计算的情况下实现了十位有效数字的准确度。方法iii)达到七位有效数字。计算了散射长度和有效距离。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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