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摘要
We presented a new method to solve Schrodinger equations especially for two special kinds of potentials, which are named the first and second kind of Woods-Saxon-like potentials in this paper. The Woods-Saxon-like potential characterized by a rapid increase occurred at the system's boundary varies slowly inside and quickly becomes a constant potential outside the system. The first (second) kind of Woods-Saxon-like potentials is finite (divergent) at the origin. By using an elaborately constructed multi-step potential to approximate the Woods-Saxon-like potential, we can obtain its approximate energy levels and piecewise analytical wave functions with high accuracy. To test our method, we solved the Schroumldinger equations of three systems atomic nuclei (208)Pb, hydrogen atoms, and sodium nanospheres. We found that our method works quite well and is superior to conventional numerical methods for the situation of Woods-Saxon-like potentials. Besides being able to obtain approximate piecewise analytical wave functions, our method has two explicit advantages (a) the absolute error of energy levels is controlled by the number of the potential steps of the multi-step approximate potential, and (b) the potential is not necessary to have an analytical expression.
- 出版日期2011-11
- 单位温州大学; 烟台大学; 复旦大学; 中国矿业大学（北京）
