A lower bound on the spectral gap of Schr\"odinger operators with weak potentials of compact support

In this paper we continue the study of the spectral gap of Schr"odinger operators on large intervals and subject to Neumann boundary conditions. The main goal is to derive a lower bound on the spectral gap which is polynomial in the interval length. This bound is derived for a class of bounded potentials of compact support which are weak enough in a suitable sense.