  We study a heavy-heavy-light three-body system confined to one space
dimension. Both binding energies and corresponding wave functions are obtained
for (i) the zero-range, and (ii) two finite-range attractive heavy-light
interaction potentials. In case of the zero-range potential, we apply the
method of Skorniakov and Ter-Martirosian to explore the accuracy of the
Born-Oppenheimer approach. For the finite-range potentials, we solve the
Schr\"odinger equation numerically using a pseudospectral method. We
demonstrate that when the two-body ground state energy approaches zero, the
three-body bound states display a universal behavior, independent of the shape
of the interaction potential.
