薛定谔方程高斯基的观测
Observations on Gaussian bases for Schrodinger's equation
摘要：
Garashchuk和Light在J.Chem.Phys.114（2001）3929中给出了用于生成多维薛定谔本征问题的有效函数空间的少数方法之一。它们的高斯基函数在高势区更宽、更稀疏，在低势区更窄、更密集。我们建议修改他们的方法基于以下观察：在非常陡峭的潜在区域，广泛的，稀疏的，高斯应该避免，即使他们的中心具有高的潜在价值。我们的数值结果表明，一个显着的提高精度可以通过这种方式获得。我们还比较的错误的配置的Galerkin方法，测试的标准缩放高斯宽度的基础上偏离正交的配置特征函数，并提出了一个标准缩放高斯宽度的基础上的哈密顿跟踪最小化。
英文摘要：
One of the few methods for generating efficient function spaces for multi-D Schrodinger eigenproblems is given by Garashchuk and Light in J.Chem.Phys. 114 (2001) 3929. Their Gaussian basis functions are wider and sparser in high potential regions, and narrower and denser in low ones. We suggest a modification of their approach based on the following observation: In very steep potential regions, wide, sparse, Gaussians should be avoided even if their centers have high potential values. Our numerical results illustrate that a dramatic improvement in accuracy may be obtained in this way. We also compare the errors of collocation to those of a Galerkin approach, test a criterion for scaling Gaussian widths based on deviation from orthogonality of collocation eigenfunctions, and suggest a criterion for scaling Gaussian widths based on Hamiltonian trace minimization.
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