Some integrable models in quantized spaces

A.N. Leznov
2002 Nuclear Physics B  
It is shown that in a quantized space determined by the B_2 (O(5)=Sp(4)) algebra with three dimensional parameters of the length L^2, momentum (Mc)^2, and action S, the spectrum of the Coulomb problem with conserving Runge-Lenz vector coincides with the spectrum found by Schrödinger for the space of constant curvature but with the values of the principal quantum number limited from the side of higher values. The same problem is solved for the spectrum of a harmonic oscillator.
doi:10.1016/s0550-3213(02)00591-6 fatcat:i6umpd737nc3vaypfpauacxc2m