Eigenvalues of any parameter in the Schrodinger radial equation
Eigenvalues of any parameter in the Schrodinger radial equation
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薛定谔径向方程中任意参数的特征值
DOI：
10.1088/0022-3700/13/23/010
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
F. Y. Hajj
中科院分区：
文献类型：
--
作者：
F. Y. Hajj
对薛定谔径向方程的解的性质进行了实验研究。从这项研究中，一个非常简单和简短的计算程序已被设计用于计算本征值和本征函数的能量，并计算本征值和本征函数的任何参数，可能存在于潜在的表达。达到9位有效数字精度的收敛迭代次数为6次（即比前一程序少1/5）。总计算时间减少了1/20。这个程序很短（大约20条语句），演示起来比描述它要容易。给出了一个例子，并给出了样本数据和测试输出。在每次迭代中，使用线性外推法求出每个特征值的试值。这种方法被发现是简单，快速，更准确的比其他方法。通过使用该程序，可以解决“逆特征值问题”。
The behaviour of the solution of the Schrodinger radial equation has been studied experimentally. From this study, a very simple and short computing program has been devised for computing the eigenvalues and eigenfunctions of the energy, and for computing the eigenvalues and eigenfunctions of any parameter that may exist in the potential expression. The number of iterations for reaching convergence to a precision of 9 significant figures is 6 (i.e. less than the previous program by a factor of 1/5). The total computing time is reduced by a factor of 1/20. This program is so short (about 20 statements) that presenting it, is easier than describing it. An example is given with sample data and test output. Linear extrapolation is used to find the trial values of each eigenvalue at each iteration. This method is found to be simpler, faster, and more accurate than other methods. By the use of this program it is possible to solve the 'inverse eigenvalue problem'.