Geodesic
The inverse problem of quantum mechanics for a~linear potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 1, pp. 74-79

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The applicability of the Gel'fand–Levitan method for solving the inverse problem in the case of potentials that increase unboundedly at infinity is demonstrated for the example of a linear potential. The following cases are considered: 1) change in the normalization of one of the eigenvalues; 2) complete elimination of one of the eigenstates; 3) inclusion in the spectrum of a new state with arbitrary energy. For all three cases, the asymptotic behavior of the new wave functions and the corrections to the reference (linear) potential are calculated. 
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     author = {V. B. Gostev and V. S. Mineev and A. R. Frenkin},
     title = {The inverse problem of quantum mechanics for a~linear potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_56_1_a6/}
}
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V. B. Gostev; V. S. Mineev; A. R. Frenkin. The inverse problem of quantum mechanics for a~linear potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 1, pp. 74-79. http://geodesic.mathdoc.fr/item/TMF_1983_56_1_a6/