求解径向薛定谔方程的梯度辛算法
Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation
摘要：
球对称势的径向薛定谔方程可以看作是具有含时弹性常数的一维经典谐振子。在求解经典动力学问题时，辛积分器以其优良的守恒性质而闻名。一类{ \it梯度}辛算法特别适合于求解谐振子动力学。利用Suzuki分解时间序算子的规则，这些算法可以很容易地应用于薛定谔方程。我们证明了这类梯度算法的力量，通过解决频谱的高度奇异的径向电位使用Killingbeck的方法向后牛顿-Rynson迭代。
英文摘要：
The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of {\it gradient} symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrodinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck's method of backward Newton-Ralphson iterations.
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