English

Scattering by many small inhomogeneities and applications

Mathematical Physics 2015-05-20 v1 Materials Science math.MP

Abstract

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 Schr\"odinger equation described by a desired potential. Similar ideas were developed by the author for acoustic and electromagnetic (EM) wave scattering problems.

Keywords

Cite

@article{arxiv.1012.2767,
  title  = {Scattering by many small inhomogeneities and applications},
  author = {A. G. Ramm},
  journal= {arXiv preprint arXiv:1012.2767},
  year   = {2015}
}
R2 v1 2026-06-21T16:57:48.634Z