Solution of the Schr\'odinger equation containing a Perey-Buck nonlocality
| Autor: | Rawitscher, George H. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysa.2012.05.001 |
| Popis: | The solution of a radial Schr\"odinger equation for {\psi}(r) containing a nonlocal potential of the form \int{K(r,r') {\psi}(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 {\psi} 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 {\psi} 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. Comment: one table, 16 figures; to be published in Nucl. Phys. A |
| Databáze: | arXiv |
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