Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators

We construct Neumann-Wigner type potentials for the massive relativistic Schrodinger operator in one and three dimensions for which an eigenvalue embedded in the bsolutely continuous spectrum exists. First we consider the relativistic variants of the original example by von Neumann and Wigner, and as a second example we discuss the potential due to Moses and Tuan. We show that in the non-relativistic limit these potentials converge to the classical Neumann-Wigner potentials. For the massless operator in one dimension we construct two families of potentials, different by the parities of the (generalized) eigenfunctions, for which an eigenvalue equal to zero or a 0-resonance exists, dependent on the rate of decay of the corresponding eigenfunctions.