A NOTE ON SCHRÖDINGER UNBOUND STATES
It is proven that all Jost solutions are unbounded for any no null complex spectral value in the upper half-plane but all of them are bounded over all values of the number line, for any real spectral value except at the null spectral value, where an additional suitable condition is required for having the same conclusion, for the unidimensional Schrödinger spectral problem type-system with potential of Faddeev-type. The proofs of these issues are based on well-known the mean value theorem as well as those of the Jost solutions. In consequence, they do not depend of the inequality where is the supreme norm of the complex matrix A and n denotes its size, by the way the inequality in [1] is fine, but as the characterization of in terms of the zeroes of however a different proof for each of them is given in the appendix of this paper (see Proposition 18 and Corollary 14, respectively).
unbound state, Jost solutions.