  We present the first exact calculation of the energy of the bound state of a
one dimensional Dirac massive particle in weak short-range arbitrary
potentials, using perturbation theory to fourth order (the analogous result for
two dimensional systems with confinement along one direction and arbitrary mass
is also calculated to second order). We show that the non--perturbative
extension obtained using Pad\'e approximants can provide remarkably good
approximations even for deep wells, in certain range of physical parameters. As
an example, we discuss the case of two gaussian wells, comparing numerical and
analytical results, predicted by our formulas.
