多个微小不均匀体的散射及其应用
Scattering by many small inhomogeneities and applications
摘要：
当散射体（非均匀体）的尺寸趋于零且其数目趋于无穷大时，多体量子力学散射问题得到了渐近解。给出了一种计算每单位体积的小不均匀性的数量及其强度的方法，使得将这些不均匀性嵌入到有界区域中导致创建一个新的系统，由所需的势描述。该系统的控制方程是由期望势描述的非相对论性薛定谔方程。类似的想法，作者开发的声波和电磁（EM）波散射问题。
英文摘要：
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small inhomogeneities per unit volume and their intensities such that embedding of these inhomogeneities in a bounded region results in creating a new system, described by a desired potential. The governing equation for this system is a non-relativistic Schrödinger equation described by a desired potential. Similar ideas were developed by the author for acoustic and electromagnetic (EM) wave scattering problems.
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