Least squares B-spline solutions of the radial Dirac equation in the continuum

D. Toffoli; P. Decleva

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Least squares B-spline solutions of the radial Dirac equation in the continuum

机译：连续统中径向Dirac方程的最小二乘B样条解

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The B-spline least-squares approach for the determination of the continuum wavefunctions which proves to be very accurate and numerically stable in the non-relativistic case has been generalized to the relativistic case. The least-squares scheme has been tested in the tree-particle and Coulomb problems. Expression of relativistic Coulomb functions in terms of the corresponding non relativistic ones is spelled out in detail and employed for testing the spline solutions. The convergence properties of the algorithm with respect to the B-spline order and the radial grid are also analyzed.

机译：用于确定连续波函数的B样条最小二乘法在非相对论情况下被证明是非常准确且数值稳定的，已被推广到相对论情况。最小二乘方案已在树粒子和库仑问题中进行了测试。详细阐述了相对论库仑函数相对于非相对论函数的表达，并用于测试样条解。还分析了算法相对于B样条阶和径向网格的收敛性。

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《Computer physics communications》 |2003年第2期|共14页
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D. Toffoli; P. Decleva;
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1. Least squares B-spline solutions of the radial Dirac equation in the continuum [J] . D. Toffoli, P. Decleva Computer physics communications . 2003,第2期

机译：连续统中径向Dirac方程的最小二乘B样条解
2. Kinetically balanced B-spline expansions in radial dirac equation [J] . Igarashi A Journal of the Physical Society of Japan . 2007,第5期

机译：径向狄拉克方程中的动力学平衡B样条展开
3. B-spline expansions in radial Dirac equation [J] . Igarashi A Journal of the Physical Society of Japan . 2006,第11期

机译：径向Dirac方程中的B样条展开
4. Generalized Solutions and Distributional Shadows for Dirac Equations [C] . Günther Hormann, Christian Spreitzer International Society for Analysis, Applications, and Computation Congress . 2019

机译：DIRAC方程的广义解决方案和分布阴影
5. A suite of MATLAB functions for the solution of linear systems of equations arising from collocation with B-splines and with monomial splines. [D] . Ghanam, Rania. 2007

机译：一组MATLAB函数，用于求解由B样条和单项样条搭配产生的线性方程组。
6. Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay [O] . Erdal Korkmaz -1

机译：时滞非线性四阶微分方程解的导数的稳定性和平方可积性。
7. Dirac reduced radial equations and the problem of additional solutions [O] . Khelashvili, Anzor, Nadareishvili, Teimuraz 2017

机译：狄拉克减少了径向方程和其他解决方案的问题
8. Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations [R] . Esteban, M. J. , Georgiev, V. , Sere, E. 1995

机译：maxwell-Dirac和Klein-Gordon-Dirac方程的固定解

Least squares B-spline solutions of the radial Dirac equation in the continuum

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