Geodesic
Algebraic quantum Hamiltonians on the~plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 57-70

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

We consider second-order differential operators $P$ with polynomial coefficients that preserve the vector space $V_n$ of polynomials of degrees not greater than $n$. We assume that the metric associated with the symbol of $P$ is flat and that $P$ is a potential operator. In the case of two independent variables, we obtain some classification results and find polynomial forms for the elliptic $A_2$ and $G_2$ Calogero–Moser Hamiltonians and for the elliptic Inozemtsev model.
Keywords: differential operator with polynomial coefficients, polynomial form of Calogero–Moser operators.
Mots-clés : classification 
@article{TMF_2015_184_1_a2,
     author = {V. V. Sokolov},
     title = {Algebraic quantum {Hamiltonians} on the~plane},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {57--70},
     publisher = {mathdoc},
     volume = {184},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a2/}
}
TY  - JOUR
AU  - V. V. Sokolov
TI  - Algebraic quantum Hamiltonians on the~plane
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 57
EP  - 70
VL  - 184
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a2/
LA  - ru
ID  - TMF_2015_184_1_a2
ER  - 
%0 Journal Article
%A V. V. Sokolov
%T Algebraic quantum Hamiltonians on the~plane
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 57-70
%V 184
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a2/
%G ru
%F TMF_2015_184_1_a2
V. V. Sokolov. Algebraic quantum Hamiltonians on the~plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a2/