  The physical properties of the edge states of the cut two-leg spin ladder are
investigated by means of the bosonization approach. By carefully treating
boundary conditions, we derive the existence of spin-1/2 edge states in the
spin ladder with a ferromagnetic rung exchange and for the open spin-1
Heisenberg chain. In contrast, such states are absent in the antiferromagnetic
rung coupling case. The approach, based on a mapping onto decoupled
semi-infinite off-critical Ising models, allows us to compute several physical
quantities of interest. In particular, we determine the magnetization and
dimerization profiles of the cut two-leg spin ladder and of the open
biquadratic spin-1 chain in the vicinity of the SU(2)$_2$ WZNW critical point.
