Comment on radiative corrections to the energy levels of "murium": An electron bound by its image charge to a wall

Starting from a completely relativistic single-particle theory and also from the full field theory we examine the radiative corrections to electron energy levels in the presence of a perfectly conducting wall. We also solve the nonrelativistic Schrödinger equation exactly for the potential $\frac{-e^2}{4z}+\frac{e^2}{4\pi m{z}^2}$. Our results agree with the conclusions of Shakeshaft and Spruch [Phys. Rev. A 22, 811 (1980)] concerning the size of the radiative level shift.