Abstract
The one-dimensional Schrödinger equation is considered when the potential is asymptotic to a positive constant on the right half line in a certain sense. The zero-energy limits of the scattering coefficients are obtained under weaker assumptions than used elsewhere, and the continuity of the scattering coefficients from the left are established. The scattering coefficients for the potential are expressed in terms of the corresponding coefficients for the pieces of the potential on the positive and negative half lines. The number of bound states for the whole potential is related to the number of bound states for the two pieces. Finally, an improved result is given on the small-energy asymptotics of reflection coefficients for potentials supported on a half line.
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