Elastic electron-deuteron scattering as a probe of the deuteron wave function

Relativistic corrections to the electric deuteron form factors are rederived within the framework of particle quantum mechanics. In addition to the kinematic corrections there are necessarily dynamic corrections that are substantially larger. For local potentials the results are identical to those derived by Gross from field theory. The reasons for the agreement of two apparently very different theories are examined in detail. The quantitative aspect of these results are illustrated by several numerical examples. A precise measurement of the polarization cross section for $q^2<13\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$ could serve to significantly restrict the shape of admissible deuteron wave functions.