  We report simple expressions for the exchange coupling in double quantum dots
calculated within the Heitler-London and the Hund-Mulliken approximations using
four different confining potentials. At large interdot distances and at large
magnetic fields the exchange coupling does not depend significantly on the
details of the potentials. In contrast, at low fields and short distances
different behaviors of the exchange coupling can be attributed to particular
features of the potentials. Our results may be useful as guidelines in
numerical studies and in the modeling of experiments.
