Geodesic
Reconstruction of confining or attractive potentials of one-dimensional Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 3, pp. 472-480

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The dependence of confining or attractive potentials on the characteristics of the discrete spectrum of the one-dimensional Schrödinger equation is investigated. Asymptotic expressions are obtained for the regular solutions and the corrections to the potential in different cases of variation of the spectral characteristics. The connection between one-parameter transformations of the normalization constants and the nonlinear evolution equations for the recovered potential is considered. 
@article{TMF_1985_62_3_a12,
     author = {V. B. Gostev and A. R. Frenkin},
     title = {Reconstruction of confining or attractive potentials of one-dimensional {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {472--480},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_62_3_a12/}
}
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V. B. Gostev; A. R. Frenkin. Reconstruction of confining or attractive potentials of one-dimensional Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 3, pp. 472-480. http://geodesic.mathdoc.fr/item/TMF_1985_62_3_a12/