Potentials with Identical Scattering Properties Below a Critical Energy

Abstract

A pair of scattering potentials are called $\alpha$-equivalent if they have identical scattering properties for incident plane waves with wavenumber $k\le \alpha$ (energy $k^2\le {\alpha }^2$.) We use a recently developed multidimensional transfer-matrix formulation of scattering theory to obtain a simple criterion for $\alpha$-equivalence of complex potentials in two and three dimensions.

9 pages

References in corpus (3)

• The transfer matrix: a geometrical perspective
• Bidirectional invisibility in Kramers-Kronig optical media
• A Class of Exactly Solvable Scattering Potentials in Two Dimensions, Entangled State Pair Generation, and a Grazing Angle Resonance Effect

Cited by in corpus (1)

• Transmission of low-energy scalar waves through a traversable wormhole