在局域子空间中计算给定范围内的能量本征值  

A direct calculation of eigenvalues of any arbitrary range of energy within local-subspace

作　　者：凤尔银 郑贤锋[2] 季学韩[2] 崔执凤 张为俊[1] 

机构地区：[1]中国科学院安徽光学精密机械研究所,合肥230031 [2]安徽师范大学物理与电信学院,安徽芜湖241000

出　　处：《原子与分子物理学报》2002年第4期522-526,共5页Journal of Atomic and Molecular Physics

基　　金：安徽省教育厅自然科学研究基金 (2 0 0 1kj111zc);安徽省重点学科资助项目

摘　　要：通过能量算符δ函数作用于完全随机格点波函数 ,构造了可用于直接计算给定范围 [Emin,Emax]内能量本征值和本征函数的局域子空间。在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示 ,讨论了广义本征值问题的解法。以Morse势和HenonAn direct theoretical calculation of eigenvalues and eigenfunctions in any arbitrary range of energy is proposed. The calculation produce a small local basis set (nonorthogonal) by applying the Chebyshev polynomials expansion of the Greens operator on a completely random grid wavefunction. The analytic expressions of matrix element of Hamilton H, overlap S are then derived directly in this nonorthoganal basis set, and the corresponding generalized eigenvalue problem is solved to give the eigenvalues and eigenfunctions within range of [ E min , E max ]. The calculation requires a minimal storage because a discrete position grid representation of the H,S is used. Two instructive examples, the one dimension Morses potential and two dimension Henon Heiles potential are considered for four energy ranges in the present study. The method proves to be efficient, straightforward and simple.

关 键 词：局域子空间 计算 给定范围 能量本征值 Green算符 CHEBYSHEV多项式 分立位置表象 广义本征值方程 分子光谱 

分 类 号：O561.3[理学—原子与分子物理]