Aktosun, Tuncay Bound states and inverse scattering for the Schrödinger equation in one dimension. (English) Zbl 0822.34070 J. Math. Phys. 35, No. 12, 6231-6236 (1994). Summary: The one-dimensional Schrödinger equation is considered when the potential and its first moment are absolutely integrable. When the potential has support contained on the left (right) half-line, it is uniquely constructed by using only the reflection coefficient from the right (left). The bound state norming constants determine whether the potential has support contained on a half-line or on the full-line. The bound state energies and the unique set of norming constants yielding the potential with support contained on the left (right) half-line are completely determined by the reflection coefficient from the right (left). An explicit example is provided. Cited in 8 Documents MSC: 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 81U40 Inverse scattering problems in quantum theory 34A55 Inverse problems involving ordinary differential equations Keywords:one-dimensional Schrödinger equation; bound state energies; norming constants; potential PDF BibTeX XML Cite \textit{T. Aktosun}, J. Math. Phys. 35, No. 12, 6231--6236 (1994; Zbl 0822.34070) Full Text: DOI OpenURL References: [1] DOI: 10.1063/1.529883 · Zbl 0762.35075 [2] Levinson N., Kgl. Danske Viden. Sels. Mat. Fys. Medd. 25 pp 1– (1949) [3] Faddeev L. D., Am. Math. Soc. Transl. 2 pp 139– (1964) [4] DOI: 10.1002/cpa.3160320202 · Zbl 0388.34005 [5] DOI: 10.1063/1.524447 · Zbl 0446.34029 [6] DOI: 10.1103/PhysRev.101.1588 [7] DOI: 10.1063/1.530089 · Zbl 0777.34056 [8] DOI: 10.1007/BF01203119 · Zbl 0790.47012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.