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.
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}
}