含Perey-Buck非定域的薛定谔方程的解
Solution of the Schrödinger equation containing a Perey-Buck nonlocality
摘要：
本文用两种方法高精度地求出了含\int{K(r,r') ψ(r') dr'}形式非定域势的径向薛定谔方程的解。Perey-Buck非局部性的应用，而不使用本地等价表示。第一种方法包括在一组Chebyshev多项式中展开，并数值求解展开系数的矩阵方程。根据所采用的多项式的数量，获得了1：10^{6}到1：10^{14}之间的精度。第二种方法包括在扩展到一组N Sturmian函数的正能量，补充迭代过程。对于N=15，无需迭代即可获得1：10^{4}的精度。在一次迭代之后，精度增加到1：10^{6}。该方法适用于一般的非定域性K。
英文摘要：
The solution of a radial Schrödinger equation for ψ(r) containing a nonlocal potential of the form \int{K(r,r') ψ(r') dr'} is obtained to high accuracy by means of two methods. An application to the Perey-Buck nonlocality is presented, without using a local equivalent representation. The first method consists in expanding ψ in a set of Chebyshev polynomials, and solving the matrix equation for the expansion coefficients numerically. An accuracy of between 1:10^{6} to 1:10^{14} is obtained, depending on the number of polynomials employed. The second method consists in expanding ψ into a set of N Sturmian functions of positive energy, supplemented by an iteration procedure. For N=15 an accuracy of 1:10^{4} is obtained without iterations. After one iteration the accuracy is increased to 1:10^{6}. The method is applicable to a general nonlocality K.
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