【摘要】 提出一种新的高精度、高效率求解一维Schrdinger方程的Obrechkoff两步方法.通过增加奇数次高阶微商项,大幅度提高了经典Obrechkoff两步递推公式的精度.由求解Morse势束缚态本征值的数值例子表明,在精度和效率上该方法比经典方法求解一维Schrdinger方程有明显的优势.更多还原

【Abstract】 In this paper,a new kind of P-stable two-step Obrechkoff method for the ultra-high-accurate solution of a one-dimensional Schrdinger equation is proposed.Improving Wang’s method,a new P-stable two-step Obrechkoff method by adding odd derivatives of higher-order has been developed.The proposed method is effective but has high local truncation error.By using the new approach,one can obtain solutions of the well-known one-dimensional Schrdinger equation.Numerical experiments on the well-known Morse potential demonstrate that our method has the advantage over Wang’s both in accuracy and efficiency.更多还原