The spinless relativistic Woods-Saxon problem

Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem posed by the spinless Salpeter equation and recall various elementary knowledge, considerations and techniques that practitioners seeking solutions to this specific reduction of the Bethe-Salpeter equation may find helpful.