Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy Dispersion Relations for the Fast Decaying Potentials

Piotr G. Grinevich, Roman G. Novikov

For the two-dimensional Schrödinger equation $$[-\Delta +v(x)]\psi =E\psi ,x\in {\mathbb{R}}^2,E=E_{fixed}>0(\ast )$$ at a fixed positive energy with a fast decaying at infinity potential $v(…