Geodesic
Monodromy-free Schrödinger operators with quadratically increasing potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 374-386 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider one-dimensional monodromy-free Schrödinger operators with quadratically increasing rational potentials. It is shown that all these operators can be obtained from the operator $-\partial^2+x^2$ by finitely many rational Darboux transformations. An explicit expression is found for the corresponding potentials in terms of Hermite polynomials. 
@article{TMF_1999_121_3_a2,
     author = {A. A. Oblomkov},
     title = {Monodromy-free {Schr\"odinger} operators with quadratically increasing potentials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {374--386},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/}
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A. A. Oblomkov. Monodromy-free Schrödinger operators with quadratically increasing potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 374-386. http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/

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