Quasi-one-dimensional excitons in a GaAs-AlxGa1-xAs quantum well are s
tudied; they are produced by an applied twin-split-gate potential whic
h confines the particles laterally and allows free motion in one dimen
sion. A variational approach is used to calculate the binding energies
E(ex) and oscillator strength f(ex) of these excitonic transitions as
functions of the applied voltage and width of the induced potential w
ells. In the limit of high electrostatic confinement the excitons are
strongly polarized and the system resembles a type II structure where
electron and hole are spatially separated. The resulting E(ex) and f(e
x) show a strong dependence on applied voltage and structure width. St
rong oscillations are found, which should be observed experimentally,
as a consequence of subtle competition between confinement and Coulomb
attraction.