Mapped Finite Element Discrete Variable Representation

为 Schr 的有效数字解答者 ? dinger 方程在物理和化学是很重要的。有限元素分离可变表示(FEDVR ) 被 Rescigno 和 McCurdy 首先建议[Phys。加快。一 62， 032706 (2000 )] 为解决散布问题的 quantummechanical。在这个工作，在一个印射的坐标的一个 FEDVR 方法被建议改进原来的 FEDVR 方法的效率。为数字示范，建议途径被申请解决氢原子的电子特徵函数和有 longrange 相互作用潜力的 Cs2 分子的电子州的 3g + 的震动的状态。数字结果显示原来的 FEDVR 的数字效率就用我们的建议印射的并列计划被改进了。

Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. 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 3E＋ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.