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Abstract: The one-dimensional Schrodinger 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 bound-state energies, knowledge of the potential on a finite interval, and all of the bound-state norming constants except one. It is shown that a missing norming constant in the data can cause at most a double nonuniqueness in the... (Update)
Active bibliography (related documents): More All
1.5: Inverse Spectral Analysis With Partial Information On The.. - Gesztesy, Simon (1997) (Correct)
1.2: Inverse Schrödinger Scattering On The Line With Partial.. - Aktosun (1996) (Correct)
0.6: Integral Equation Methods For The Inverse Problem With.. - Aktosun, Klaus (1996) (Correct)
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0.9: Scattering for the Forced Non-Linear Schrodinger Equation with a.. - Weder (Correct)
0.5: The Time-Dependent Approach to Inverse Scattering - Weder (Correct)
0.2: Inverse Two Cluster Scattering - Enss, Weder (1996) (Correct)
BibTeX entry: (Update)
@misc{ aktosun-inverse,
author = "Tuncay Aktosun and Ricardo Weder",
title = "Inverse Scattering with Partial Information on the Potential",
url = "citeseer.ist.psu.edu/436252.html" }
Citations (may not include all citations):44 Inverse scattering on the line (context) - Deift, Trubowitz - 1979
42 Sturm-Liouville operators and applications (context) - Marchenko - 1986
40 Inverse problems in quantum scattering theory (context) - Chadan, Sabatier - 1989
15 Inverse spectral analysis with partial information on the po.. - Gesztesy, Simon - 1997
15 Quantum Mechanics (context) - Merzbacher - 1970
11 matrix of the one-dimensional Schrodinger equation (context) - Faddeev, the - 1967
9 A factorization of the scattering matrix for the Schrodinger.. (context) - Aktosun - 1992
7 Operator methods for inverse scattering on the real line (context) - Melin - 1985
6 the Riemann-Hilbert problem for the one-dimensional Schrodin.. (context) - Aktosun, Klaus et al. - 1993
5 Bound states and inverse scattering for the Schrodinger quat.. (context) - Aktosun - 1994
4 Reconstruction of a potential on the line that is a priori k.. (context) - Gr'ebert, Weder - 1995
3 the determination of potentials without bound state data (context) - Rundell, Sacks - 1994
2 Inverse Schrodinger scattering on the line with partial know.. - Aktosun - 1996
1 Uniqueness of the solution of the onedimensional problem of .. (context) - Novikova, Markushevich - 1987
1 the number of bound states for the one-dimensional Schroding.. (context) - Aktosun, Klaus et al. - 1998
1 Inverse theory: problem on the line (context) - Aktosun, Klaus
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