SPARSE：从径向Schrödinger方程求解散射极点和振幅
SPARSE: Scattering Poles and Amplitudes from Radial Schrödinger Equations
AI总结：
本文提出用有限差分法求解径向Schrödinger方程，用于计算具有自旋的粒子在定总角动量部分波中的非弹性散射极点和振幅。
摘要：
本文提出了一种利用有限差分法求解径向Schrödinger方程的算法，用于计算具有自旋的粒子在定总角动量部分波中的非弹性散射极点和振幅。通过在原点和任意大半径处施加狄利克雷边界条件，将微分方程组近似为一个普通的线性非齐次系统。通过将数值解与远距离处的解析实解进行比较，计算出物理能量下的K矩阵。然后从物理K矩阵中计算散射极点和振幅。
英文摘要：
We introduce an algorithm for the solution of a system of radial Schrödinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations is approximated as an ordinary linear nonhomogeneous system using the finite difference method. Dirichlet boundary conditions are imposed at the origin and at an arbitrary large radius. The numerical wavefunction is calculated using LAPACK general banded LU decomposition routines. The $K$-matrix for physical energies is calculated from the numerical solutions of the system by least-square fit to the analytical real solutions at large distances. The scattering amplitudes for physical energies is then calculated from the $K$-matrix. Scattering poles in the lower half of the unphysical Riemann sheet are calculated by numerical extrapolation of the scattering amplitudes using the AAA algorithm for rational approximation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
