A novel method for the solution of the Schrödinger equation in the presence of exchange terms

• Published in: The Journal of chemical physics 2003-05, Vol.118 (20), p.9149-9156
• Main Authors: Rawitscher, George H., Kang, S.-Y., Koltracht, I.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.1567254

In the Hartree–Fock approximation the Pauli exclusion principle leads to a Schrödinger equation of an integro-differential form. We describe the extension of a new spectral noniterative method (S-IEM), previously developed for solving the Lippmann–Schwinger integral equation with local potentials, 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 two other methods. One is a noniterative solution 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 S-IEM method turns out to be more accurate than the two comparison methods by many orders of magnitude for the same number of mesh points.