Symmetries in Scalar Potential Scattering

The elastic scattering of the mass-less (${\mit\omega}^2 = c^2 k^2$) complex scalar field by a potential, $q[.]$, of bounded support is a prototype model which finds applications to acoustics and electromagnetics in a classical (i.e., non quantum mechanical) setting. Of particular interest are the symmetries of the scattered wave, $u[.]$ and of the quantities derived therefrom ($A[.]$, $|A[.]|^2$) caused by symmetry operations on $q[.]$, such as translation, rotation, reflection, and scaling. This investigation is motivated by the analysis of scattering patterns of environmental interest.