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Mapped Finite Element Discrete Variable Representation
De-quan Yu,Shu-lin Cong*,Dong H. Zhang,Zhi-gang Sun*
Author NameAffiliationE-mail
De-quan Yu School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, ChinaState Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chines  
Shu-lin Cong* School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China shlcong@dlut.edu.cn 
Dong H. Zhang State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China  
Zhi-gang Sun* State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China zsun@dicp.ac.cn 
Abstract:
Efficient numerical solver for the Schr?dinger equation is very important in physics and chem-istry. The finite element discrete variable representation (FE-DVR) was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 (2000)] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 33gof the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numeri-cal efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme
Key words:  Discrete variable representation, Mapped Fourier method, Ultra-cold atomic photoassociation, Schrodinger equation solver, Singularity of Coulomb potential
FundProject:
求解薛定锷方程的有限元离散格点表象
于德权,丛书林*,张东辉,孙志刚*
摘要:
提出了利用映射函数来调节有限元离散格点表象的格点分布,从而提高其数值效率.为了测试该新方法的数值效率,将其用于氢原子中电子的本征态和本征能量以及具有长程势的Cs2分子三重态的振动能级的求解,并与最初的有限元离散格点表象方法作了比较.计算结果表明:利用格点映射的方法可以显著提高限元离散格点表象的数值效率
关键词:  离散格点表象,映射傅立叶网格,超冷原子光缔合,薛定锷方程,库伦奇点
DOI:10.1063/1674-0068/26/06/755-764
分类号: