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是一款可在任意维度与多种坐标系下求解广义非齐次含时薛定谔类方程i∂Ψ/∂t = H[t, Ψ] + Φ的C++代码。哈密顿量H[t, Ψ]可包含简单非线性项，例如格罗斯-皮塔耶夫斯基（Gross-Pitaevskii）与哈特里（-福克）类问题。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、双光电子发射过程。该代码专为大规模从头算（ab initio）、模型探索以及计算物理进阶教学设计。其独具特色的数值方法包括用于计算单、双发射谱的含时表面通量法，以及用于吸收处理的外复标度法。波函数与算子通过树形结构进行管理，并在粗粒度层级系统性地运用递归运算。数值离散、解析离散与基于网格的离散方法可灵活结合，并在统一的抽象层级下进行统一处理。算子可通过集成符号代数的脚本语言在输入文件中指定。该代码在设计之初即集成了友好的输入输出接口、完善的错误防护机制与完整的文档。