AI 中文总结
本文提出 SWORD 方法，在 Weyl 表示下将 Dirac 方程精确约化为二分量形式，避免逆势算子，并通过 Helmholtz 格林函数迭代求解，在自适应多小波框架中实现，以高精度和效率处理相对论量子化学问题。
AI 中文摘要
我们提出了一种在 Weyl 表示下对 Dirac 方程进行精确自洽二分量重构的方法。通过利用 Weyl 基中动能算子的对角结构以及纯标量质量耦合，四分量 Dirac 问题被约化为精确的二分量形式，而无需引入传统能量解耦方法中出现的逆势算子。所得的二阶微分方程被转化为积分形式，并通过与 Helmholtz 格林函数卷积进行迭代求解。我们在自适应多小波基框架内实现了这一形式体系，提供了严格的、用户定义的误差控制。针对简单原子系统的概念验证计算展示了所提算法的数值稳定性、准确性和效率。
英文摘要
We present an exact self-consistent two-component reformulation of the Dirac equation in the Weyl representation. By exploiting the diagonal structure of the kinetic operator and the purely scalar mass coupling in the Weyl basis, the four-component Dirac problem is reduced to an exact two-component form without introducing inverse-potential operators that arise in conventional energy-decoupling approaches. The resulting second-order differential equations are cast into an integral formulation and solved iteratively via convolution with the Helmholtz Green's function. We implement this formalism within an adaptive multiwavelet basis framework, providing rigorous, user-defined error control. Proof-of-concept calculations for simple atomic systems demonstrate the numerical stability, accuracy, and efficiency of the proposed algorithm.
CommentsDraft version, might be further improved with even more data
