Increase of the binding energy of an electron by coupling to a photon field

Abstract

We look at an electron in the field of an arbitrary external potential $V$, such that the Schrödinger operator $p^2 + V$ has at least one eigenvalue, and show that by coupling to a quantized radiation field the binding energy increases, at least for small enough values of the coupling constant $α$. Moreover, we provide concrete numbers for $α$, the ultraviolet cut-off $Λ$, and the radiative correction for which our procedure works.