  With a Green's function formalism we obtain the eigenvalue spectrum of a
tight-binding one-dimensional exciton model characterized by a contact
interaction, a Coulombic electron and hole attraction, the Heller-Marcus
exciton-hopping energy and an external constant and homogeneous electric field.
The resulting eigenvalue spectrum, in the form of an unevenly spaced
Wannier-Stark ladder with envelope profiles, is used to obtain the effective
mass of the exciton by the application of the Mattis-Gallinar effective mass
formula [D. C. Mattis and J.-P. Gallinar, {\it Phys. Rev. Lett.} {\bf{53}},
1391 (1984)]. We obtain positive and negative effective masses for the exciton.
The inverse effective mass may oscillate periodically as a function of the
inverse of the electric field, with the frequency of oscillation linearly
dependent upon the tight-binding hopping matrix element. The exciton radius is
also obtained with the Green's function formalism, and it too exhibits
Keldysh-like field dependent oscillations, as well as abrupt variations
associated to strongly avoided crossings in the eigenvalue spectrum. Finally,
some comments are made about the experimental relevance of our results.
