论文标题
一维固定式狄拉克运算符的透射操作员的分析近似以及用于解决初始价值和光谱问题的应用
Analytic approximation of transmutation operators for one-dimensional stationary Dirac operators and applications to solution of initial value and spectral problems
论文作者
论文摘要
提出了一种基于trans变运算符的分析近似的一维dirac方程的初始值和频谱问题的近似解决方案的方法。实际上，通过与Arxiv中引入的广义正式功能相关的矩阵有价值函数的有限线性组合，将解决方案的数值近似值降低为势矩阵的近似值。就电势平滑度而言，收敛率估计已得到证明。该方法允许人们以极高的精度计算较低和更高的特征。
A method for approximate solution of initial value and spectral problems for one dimensional Dirac equation based on an analytic approximation of the transmutation operator is presented. In fact the problem of numerical approximation of solutions is reduced to approximation of the potential matrix by a finite linear combination of matrix valued functions related to generalized formal powers introduced in arXiv:1904.03361. Convergence rate estimates in terms of smoothness of the potential are proved. The method allows one to compute both lower and higher eigendata with an extreme accuracy.
