Geodesic
Monodromy-free Schr\"odinger operators with quadratically increasing potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 374-386

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {121},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/}
}
TY  - JOUR
AU  - A. A. Oblomkov
TI  - Monodromy-free Schr\"odinger operators with quadratically increasing potentials
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1999
SP  - 374
EP  - 386
VL  - 121
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/
LA  - ru
ID  - TMF_1999_121_3_a2
ER  - 
%0 Journal Article
%A A. A. Oblomkov
%T Monodromy-free Schr\"odinger operators with quadratically increasing potentials
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1999
%P 374-386
%V 121
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/
%G ru
%F TMF_1999_121_3_a2
A. A. Oblomkov. Monodromy-free Schr\"odinger 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/