Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator - art. no. 032509

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable a ngular momentum values. At the aphelion (perihelion) points of classical or bits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillato r are still conserved. For the screened two-dimensional (2D) Coulomb potent ial and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU( 2) are still preserved at the aphelion (perihelion) points of classical orb its, respectively. For the screened 3D Coulomb potential, the dynamical sym metry SO4 is also preserved at the aphelion (perihelion) points of classica l orbits. But for the screened 3D isotropic harmonic oscillator, the dynami cal symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb p otential and isotropic harmonic oscillator, only the energy (but not angula r momentum) raising and lowering operators can be constructed from a factor ization of the radial Schrodinger equation.