Geodesic
Inverse scattering problem for the~Schr\"odinger equation with an~additional quadratic potential on the~entire axis
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 1, pp. 54-63

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We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.
Keywords: Schrödinger equation, oscillator, inverse scattering problem, basic equation.
Mots-clés : reflection coefficient 
@article{TMF_2018_195_1_a4,
     author = {I. M. Guseinov and A. Kh. Khanmamedov and A. F. Mamedova},
     title = {Inverse scattering problem for {the~Schr\"odinger} equation with an~additional quadratic potential on the~entire axis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_1_a4/}
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I. M. Guseinov; A. Kh. Khanmamedov; A. F. Mamedova. Inverse scattering problem for the~Schr\"odinger equation with an~additional quadratic potential on the~entire axis. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 1, pp. 54-63. http://geodesic.mathdoc.fr/item/TMF_2018_195_1_a4/