tRecX — An environment for solving time-dependent Schrödinger-like problems

tRecX is a C++ code for solving generalized inhomogeneous time-dependent Schrödinger-type equations idΨ/dt = H[t, Ψ] + Φ in arbitrary dimensions and in a variety of coordinate systems. The operator H[t, Ψ] may have simple non-linearities, as in Gross-Pitaevskii and Hartree(-Fock) problems. Primary application of tRecX has been non-perturbative strong-field single and double photo-electron emission in atomic and molecular physics. The code is designed for large-scale ab initio calculations, for exploring models, and for advanced teaching in computational physics. Distinctive numerical methods are the time-dependent surface flux method for the computation of single and double emission spectra and exterior complex scaling for absorption. Wave functions and operators are handled by tree-structures with the systematic use of recursion on the coarse-grain level. Numerical, analytic, and grid-based discretizations can be combined and are treated on the same abstract level. Operators are specified in the input using a script language including symbolic algebra. User-friendly in- and output, error safety, and documentation are integrated by design.tRecX是一款用于求解任意维度、多种坐标系下广义非齐次含时薛定谔型方程（generalized inhomogeneous time-dependent Schrödinger-type equations）$ifrac{partial Psi}{partial t} = H[t, Psi] + Phi$的C++代码。其哈密顿算符$H[t, Psi]$可包含简单非线性项，如格罗斯-皮塔耶夫斯基（Gross-Pitaevskii）与哈特里（-福克）（Hartree(-Fock)）问题中的形式。tRecX的核心应用场景为原子与分子物理领域中的非微扰强场单光电子与双光电子发射过程。该代码专为大规模从头算（ab initio）计算、模型探索以及计算物理的进阶教学设计。其独具特色的数值方法包括用于计算单、双光电子发射谱的含时表面通量法（time-dependent surface flux method），以及用于吸收处理的外复标度法（exterior complex scaling）。波函数与算符通过树状结构进行管理，并在粗粒度层面系统性地运用递归操作。数值离散、解析处理与基于网格的离散化方法可相互结合，并在统一的抽象层面进行处理。算符可通过集成符号代数功能的脚本语言在输入文件中进行定义。该代码在设计之初即集成了友好的人机交互输入输出、错误安全机制与完整文档。