  We study the ground state and low-energy subgap excitations of a finite wire
of a time-reversal-invariant topological superconductor (TRITOPS) with
spin-orbit coupling. We solve the problem analytically for a long chain of a
specific one-dimensional lattice model in the electron-hole symmetric
configuration and numerically for other cases of the same model. We present
results for the spin density of excitations in long chains with an odd number
of particles. The total spin projection along the axis of the spin-orbit
coupling $S_z= \pm 1/2$ is distributed with fractions $\pm 1/4$ localized at
both ends, and shows even-odd alternation along the sites of the chain. We
calculate the localization length of these excitations and find that it can be
well approximated by a simple analytical expression. We show that the energy
$E$ of the lowest subgap excitations of the finite chain defines tunneling and
entanglement between end states.We discuss the effect of a Zeeman coupling
$\Delta_Z$ on one of the ends of the chain only. For $\Delta_Z<E$, the energy
difference of excitations with opposite spin orientation is $\Delta_Z/2$,
consistent with a spin projection $\pm 1/4$. We argue that these physical
features are not model dependent and can be experimentally observed in TRITOPS
wires under appropriate conditions.
