AI 中文总结
研究量子散射和电磁系统中共振态的范数问题，通过用边界积分代替体积积分的方法，应用于量子粒子和电磁系统的多种物理设置，如处理不同势及形状的腔体等。
AI 中文摘要
共振态在空间上发散，因此不是平方可积的。相反，它们的范数由左右态的双正交标量积定义。在分段均匀系统中，我们用一个方便的边界积分代替相应的体积积分，并将此过程应用于各种物理设置。对于任意维度的量子粒子，我们处理硬壁和分段常数势。对于具有分段均匀材料特性的电磁系统，我们考虑任意形状的三维和有效二维腔体。例如，我们处理球形散射体和圆盘。
英文摘要
Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral by a convenient boundary integral in piecewise homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise constant potentials. For electromagnetic systems with piecewise homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities of arbitrary shape. As examples, we treat the spherical scatterer and the circular disk.
Comments28 pages, 1 figure
