 01100 T. Aktosun and R. Weder
 Inverse Scattering with Partial Information on the Potential
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Mar 14, 01

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Abstract. The onedimensional Schr\"{o}dinger equation is considered
when the potential is real valued and integrable and has a finite
first moment. The recovery of such a potential is analyzed
in terms of the scattering data consisting of a
reflection coefficient, all the
boundstate energies, knowledge of the potential
on a finite interval, and all of the
boundstate norming constants except one.
It is shown that a missing norming constant in the data can cause at most
a double nonuniqueness in the recovery.
In the particular case when the missing norming constant
in the data corresponds to the lowestenergy bound state,
the necessary and sufficient conditions are obtained for the
nonuniqueness, and
the two norming constants and the corresponding
potentials are determined.
Some explicit examples are provided to illustrate
the nonuniqueness.
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