提出电磁势波动方程的普适解，无需人为引入超前项即可消除奇点。
Derivation and physical interpretation of the general solutions to the wave equations for electromagnetic potentials
- 从推迟电荷电流密度出发，在倒空间求解波动方程，得到嵌套积分形式的通解。
- 解在空间上无奇点，适用于任意电荷分布，且不依赖点电荷模型的修正假设。
- 为凝聚态物理与荧光成像等应用提供新的理论工具，适合研究复杂介质中的电磁响应。
本文从推迟电荷、电流和极化密度出发，推导出标量势、矢量势和赫兹势的非齐次波动方程，并在倒空间（k-空间）中求解，获得通解。这些解以源体积、k-空间和时间上的嵌套积分为形式，本质上避免了空间奇点，无需像以往点电荷模型那样人为引入超前与推迟项的组合来消除奇点。文中结合具体例子，讨论了不同势在实空间与倒空间形式的物理含义。该方法可对任意电荷分布进行k-空间展开，有望应用于凝聚态物理及基于荧光的成像领域。
原文摘要 · Abstract (English)
The inhomogeneous wave equations for the scalar, vector, and Hertz potentials are derived starting from retarded charge, current, and polarization densities and then solved in the reciprocal (or k-) space to obtain general solutions, which are formulated as nested integrals of such densities over the source volume, k-space, and time. The solutions thus obtained are inherently free of spatial singularities and do not require introduction by fiat of combinations of advanced and retarded terms as done previously to cure such singularities for the point-charge model. Physical implications of these general solutions are discussed in the context of specific examples involving either the real or reciprocal space forms of the different potentials. The present approach allows for k-space expansions of the potentials for arbitrary distributions of charges and may lead to applications in condensed matter and fluorescence-based imaging.
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