Two Distinct Local Potentials with No Bound States Can Have the Same Scattering Operator: A Nonuniqueness in Inverse Spectral Transformations
- 29 June 1981
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 46 (26) , 1657-1659
- https://doi.org/10.1103/physrevlett.46.1657
Abstract
By giving an explicit example in one dimension, it is shown that by relaxing a condition on the ranges, at least two potentials can have the same scattering operator in some cases. The two potentials are local and do not support point eigenvalues. The implications for solutions of the Korteweg-de Vries equation are briefly discussed.Keywords
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