Geodesic
Quadratic algebras and dynamics in curved spaces.~II. The Kepler problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 396-410

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

The symmetry aspects of the Kepler problem in a space of constant negative curvature are considered. It is shown that the algebra of the hidden symmetry reduces to the quadratic Racah algebra $QR(3)$, and this makes it possible to express the coefficients of the overlapping of the wave functions in the spherical and parabolic coordinates in terms of Wilson–Racah polynomials. It is shown that the dynamical symmetry algebra that generates the spectrum is the quadratic Jacobi algebra $QJ(3)$. Its ladder operators permit explicit construction of wave functions in the coordinate representation with the ground state as the starting point. 
@article{TMF_1992_91_3_a3,
     author = {Ya. I. Granovskii and A. S. Zhedanov and I. M. Lutsenko},
     title = {Quadratic algebras and dynamics in curved {spaces.~II.} {The} {Kepler} problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {396--410},
     publisher = {mathdoc},
     volume = {91},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a3/}
}
TY  - JOUR
AU  - Ya. I. Granovskii
AU  - A. S. Zhedanov
AU  - I. M. Lutsenko
TI  - Quadratic algebras and dynamics in curved spaces.~II. The Kepler problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 396
EP  - 410
VL  - 91
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a3/
LA  - ru
ID  - TMF_1992_91_3_a3
ER  - 
%0 Journal Article
%A Ya. I. Granovskii
%A A. S. Zhedanov
%A I. M. Lutsenko
%T Quadratic algebras and dynamics in curved spaces.~II. The Kepler problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 396-410
%V 91
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a3/
%G ru
%F TMF_1992_91_3_a3
Ya. I. Granovskii; A. S. Zhedanov; I. M. Lutsenko. Quadratic algebras and dynamics in curved spaces.~II. The Kepler problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 396-410. http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a3/