## Examples of non-uniqueness in one-dimensional inverse scattering for which $$T(k)=O(k^ 3)$$ and $$O(k^ 4)$$ as k$$\to 0$$.(English)Zbl 0625.35074

An example of a one-parameter family of potentials in one-dimensional non-relativistic quantum mechanics is given such that all the potentials in the family have the same scattering matrix at all energies and the transmission coefficient behaves like $$T(k)=O(k^ 3)$$ as $$k\to 0$$. An example where $$T(k)=O(k^ 4)$$ as $$k\to 0$$ is also given.

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 81U20 $$S$$-matrix theory, etc. in quantum theory 35P25 Scattering theory for PDEs 35R30 Inverse problems for PDEs
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