A simple inquiry on the critical electric dipole moment in one space dimension

Abstract

The magnitude of an electric dipole moment must be larger or equal to a certain critical value to support bound states. This is not a widely known fact that nevertheless is easy to understand on heuristic terms and relatively easy to calculate. This critical dipole moment, $p_{C}$, has been calculated in 2 and 3 dimensions. It has been ascertained that it does not exist in one dimension or, at least, that it is not computable. In this work, after giving simple arguments on the existence of this critical moment, we compute $p_{C}$ in one dimension.