Inverse scattering for Stark Hamiltonians with short‐range potentials

Abstract

We consider the Stark Hamiltonian H=½p 2 −x 1 +V(x) which describes the scattering of a quantum mechanical particle in $\mathbb{R}^{n}$ by a short‐range potential in the presence of a constant electric field. We show that the electric potential V is uniquely determined by the high energy limit of the scattering operator, if the dimension n≥3. We prove our results using the Enss–Weder time‐dependent method.