一种求解薛定谔方程的新方法。在存在交换条件时
A Novel Method for the Solution of the Schroedinger Eq. in the Presence of Exchange Terms
摘要：
在Hartree-Fock近似中，泡利不相容原理导致薛定谔方程。的积分微分形式。我们描述了一种新的谱非迭代方法（S-IEM），以前开发的Lippman-Schwinger积分方程的局部电位，现在已经扩展到包括交换非局域性。我们将其应用于电子-氢散射的限制情况，其中束缚电子保持在基态，入射电子的角动量为零，我们比较了新方法的准确性和经济性与其他三种方法。一种是Sams和Kouri在1969年描述的积分方程的非迭代解（NIEM）。另一种是Kim和Udagawa在1990年为核物理应用引入的迭代方法，该方法将解扩展到由矩量法获得的特别有利的基。第三种方法是基于交换项的奇异值分解，然后对剩余项进行迭代。对于相同数量的网格点，S-IEM方法比上述其他三种方法中的任何一种都要精确许多数量级。
英文摘要：
In the Hartree-Fock approximation the Pauli exclusion principle leads to a Schroedinger Eq. of an integro-differential form. We describe a new spectral noniterative method (S-IEM), previously developed for solving the Lippman-Schwinger integral equation with local potentials, which has now been extended so as to include the exchange nonlocality. We apply it to the restricted case of electron-Hydrogen scattering in which the bound electron remains in the ground state and the incident electron has zero angular momentum, and we compare the acuracy and economy of the new method to three other methods. One is a non-iterative solution (NIEM) of the integral equation as described by Sams and Kouri in 1969. Another is an iterative method introduced by Kim and Udagawa in 1990 for nuclear physics applications, which makes an expansion of the solution into an especially favorable basis obtained by a method of moments. The third one is based on the Singular Value Decomposition of the exchange term followed by iterations over the remainder. The S-IEM method turns out to be more accurate by many orders of magnitude than any of the other three methods described above for the same number of mesh points.
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