Darboux transformation for the Schrödinger equation with steplike potentials

Journal of Mathematical Physics

Volumn 41, Issue 4, 2000, Pages 1619-1631

  Aktosun, Tuncay ^a  

^a NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347132     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533254     Document Type: Article

References (16)

1. P. Deift and E. Trubowitz, "Inverse scattering on the line," Commun. Pure Appl. Math. 32, 121-251 (1979).
2. K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer, New York, 1989).
3. F. Gesztesy, B. Simon, and G. Teschl, "Spectral deformations of one-dimensional Schrödinger operators," J. Anal. Math. 70, 267-324 (1996).
4. V. Buslaev and V. Fomin, "An inverse scattering problem for the one-dimensional Schrödinger equation on the entire axis," Vestn. Leningr. Univ. 17, 56-64 (1962) (Russian).
5. A. Cohen and T. Kappeler, "Scattering and inverse scattering for steplike potentials in the Schrödinger equation," Indiana Univ. Math. J. 34, 127-180 (1985).
6. J. Legendre, "Problème inverse de Schrödinger sur la ligne avec conditions dissymmétriques et applications," Ph.D. thesis, Acad. Montpellier, Univ. Sci. Tech. Languedoc, 1982.
7. T. Aktosun, "On the Schrödinger equation with steplike potentials," J. Math. Phys. 40, 5289-5305 (1999).
8. E. B. Davies and B. Simon, "Scattering theory for systems with different spatial asymptotics on the left and right," Commun. Math. Phys. 63, 277-301 (1978).
9. F. Gesztesy, R. Nowell, and W. Pötz, "One-dimensional scattering theory for quantum systems with nontrivial spatial asymptotics," Diff. Integral Eqs. 10, 521-546 (1997).
10. X. L. Zhou and S. H. Chen, "Theoretical foundations of x-ray and neutron reflectometry," Phys. Rep. 257, 223-348 (1995).
11. G. Felcher and T. Russell (eds.), "Proceedings of the workshop on methods of analysis and interpretation of neutron reflectivity data," Physica B 173 (1991).
12. G. Felcher and H. You (eds.), "Proceedings of the 4th international conference on surface x-ray and neutron scattering," Physica B 221 (1996).
13. C. F. Majkrzak and N. F. Berk, "Exact determination of the phase in neutron reflectometry," Phys. Rev. B 52, 10827-10830 (1995).
14. V. O. de Haan, A. A. van Well, P. E. Sacks, S. Adenwalla, and G. P. Felcher, "Toward the solution of the inverse problem in neutron reflectometry," Physica B 221, 524-532 (1996).
15. T. Aktosun and P. Sacks, "Phase recovery with nondecaying potentials," SIAM J. Appl. Math, (to be published).
16. T. Aktosun, M. Klaus, and C. van der Mee, "Wave scattering with absorption," J. Math. Phys. 39, 1957-1992 (1998).