Inverse Spectral Problem for the One-Dimensional Stark Operator on the Semiaxis

Abstract

We consider the Stark operator $$ T=-\frac{d^2}{dx^2}+x+q(x) $$ on the semiaxis 0 ≤ x < ∞ with Dirichlet boundary condition at the origin. By the method of transformation operators, we study the direct and inverse spectral problems, deduce the main integral equation for the inverse problem, and prove that this equation is uniquely solvable. We also propose an effective algorithm of reconstruction of the perturbation potential.