Inverse spectral problem for the~Schr\"odinger equation with an~additional linear potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 1, pp. 66-80
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We consider the one-dimensional Schrödinger equation with an additional linear potential on the whole axis and construct a transformation operator with a condition at $-\infty$. We obtain the fundamental integral Gelfand–Levitan equation on the half-axis $(-\infty,x)$ and prove the unique solvability of this fundamental equation.
Keywords:
Schrödinger equation, additional linear potential, Airy function, transformation operator, Gelfand–Levitan equation, inverse scattering problem.
@article{TMF_2020_202_1_a5,
author = {A. Kh. Khanmamedov and M. G. Makhmudova},
title = {Inverse spectral problem for {the~Schr\"odinger} equation with an~additional linear potential},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {66--80},
publisher = {mathdoc},
volume = {202},
number = {1},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a5/}
}
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%0 Journal Article %A A. Kh. Khanmamedov %A M. G. Makhmudova %T Inverse spectral problem for the~Schr\"odinger equation with an~additional linear potential %J Teoretičeskaâ i matematičeskaâ fizika %D 2020 %P 66-80 %V 202 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a5/ %G ru %F TMF_2020_202_1_a5
A. Kh. Khanmamedov; M. G. Makhmudova. Inverse spectral problem for the~Schr\"odinger equation with an~additional linear potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 1, pp. 66-80. http://geodesic.mathdoc.fr/item/TMF_2020_202_1_a5/