Inverse Schrödinger scattering on the line with partial knowledge of the potential

SIAM Journal on Applied Mathematics

Volumn 56, Issue 1, 1996, Pages 219-231

  Aktosun, Tuncay ^a  

^a NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

Bound states; Inverse scattering; Scattering; Schr dinger equation

Indexed keywords

BOUNDARY CONDITIONS; ELECTROMAGNETIC WAVE REFLECTION; ELECTRON ENERGY LEVELS; INTEGRAL EQUATIONS; INTEGRATION; INVERSE PROBLEMS; MATRIX ALGEBRA;

BOUND STATES; INVERSE SCATTERING; REFLECTION COEFFICIENT; SCHRODINGER EQUATION;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 0030086310     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994273995     Document Type: Article

References (16)

1. T. AKTOSUN, Perturbations and Stability of the Marchenko Inversion Method. Ph.D. thesis, Indiana University, Bloomington, 1986.
2. _, A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension, J. Math. Phys., 33 (1992), pp. 3865-3869.
3. _, Bound states and inverse scattering for the Schrödinger equation in one dimension, J. Math. Phys., 35 (1994), pp. 6231-6236.
4. T. AKTOSUN, M. KLAUS, AND C. VAN DER MEE, Scattering and inverse scattering in 1-D nonhomogeneous media, J. Math. Phys., 33 (1992), pp. 1717-1744.
5. _, Inverse scattering in 1-D nonhomogeneous media and the recovery of the wave-speed, J. Math. Phys., 33 (1992), pp. 1395-1402.
6. _, On the Riemann-Hilbert problem for the one-dimensional Schrödinger equation, J. Math. Phys., 34 (1993), pp. 2651-2690.
7. _, Inverse wave scattering with discontinuous wave speed, J. Math. Phys., 36 (1995), pp. 2880-2928.
8. K. CHADAN AND P. C. SABATIER, Inverse Problems in Quantum Scattering Theory, 2nd ed., Springer-Verlag, New York, 1989.
9. P. DEIFT AND E. TRUBOWITZ, Inverse scattering on the line, Comm. Pure Appl. Math., 32 (1979), pp. 121-251.
10. L. D. FADDEEV, Properties of the S matrix of the one dimensional Schrödinger equation, Amer. Math. Soc. Transl., 2 (1964), pp. 139-166 [Trudy Mat. Inst. Steklova, 73 (1964), pp. 314-336 (Russian)].
11. L. D. FADDEEV, Properties of the S matrix of the one dimensional Schrödinger equation, Amer. Math. Soc. Transl., 2 (1964), pp. 139-166 [Trudy Mat. Inst. Steklova, 73 (1964), pp. 314-336 (Russian)].
12. B. GREBERT AND R. WEDER, Reconstruction of a potential on the line that is a priori known on the half line, SIAM J. Appl. Math., 55 (1995), pp. 242-254.
13. _, manuscript in preparation, 1995.
14. V. A. MARCHENKO, Sturm-Liouville Operators and Applications, Birkhäuscr, Basel, 1986.
15. R. G. NEWTON, Inverse, scattering. I. One dimension, J. Math. Phys., 21 (1980), pp. 493-505.
16. W. RUNDELL AND P. E. SACKS, On the determination of potentials without bound state data. J. Comput. Appl. Math., 55 (1994), pp. 325-347.