Explicit scattering solutions of the one-dimensional Schrödinger equation are given. A one-parameter family of the potentials considered here causes the same scattering at all energies. The previously published explicit examples of nonuniqueness in the one-dimensional inverse quantum problem are special cases of the potentials given here.

• Received 15 December 1986

DOI:https://doi.org/10.1103/PhysRevLett.58.2159