Resonances in the one dimensional Stark effect in the limit of small field

Abstract

We discuss the resonances of Hamiltonians with a constant electric field in one dimension in the limit of small field. These resonances occur near the real axis, near zeros of the analytic continuation of a reflection coefficient for potential scattering, and near the line arg z = −2π/3. We calculate their asymptotics. In conclusion we make some remarks about the higher dimensional problem.