Geodesic
Inverse problem of reconstructing a~confining potential for the radial Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 70-79

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The problem of reconstructing a confining (increasing at infinity) potential for the radial Schrödinger equation from the spectral distribution function is considered. A perturbation to the potential that changes the first $n$ levels and normalization constants is constructed and its asymptotic behavior as $r\to\infty$ investigated. The connection between the moments of the spectral distribution function and the derivatives of the potential at the origin is established. The procedure for reconstructing an increasing potential from a finite set of experimental data is proposed. 
@article{TMF_1981_48_1_a7,
     author = {M. N. Adamyan},
     title = {Inverse problem of reconstructing a~confining potential for the radial {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {70--79},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_48_1_a7/}
}
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M. N. Adamyan. Inverse problem of reconstructing a~confining potential for the radial Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 70-79. http://geodesic.mathdoc.fr/item/TMF_1981_48_1_a7/