Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 374-386
Citer cet article
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/
@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},
year = {1999},
volume = {121},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/}
}
TY - JOUR
AU - A. A. Oblomkov
TI - Monodromy-free Schrödinger operators with quadratically increasing potentials
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1999
SP - 374
EP - 386
VL - 121
IS - 3
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 Schrödinger operators with quadratically increasing potentials
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1999
%P 374-386
%V 121
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a2/
%G ru
%F TMF_1999_121_3_a2
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.
