GROUP-APPROACH TO THE FACTORIZATION OF THE RADIAL OSCILLATOR EQUATION

This work studies a variety of factorizations for the radial isotropic oscillator Hamiltonian leading to a hierarchy of radial Hamiltonians labeled by a discrete index. These results are applied to find a relat ionship between the ladder operators (which allow one to move in the e igenfunction space of a fixed Hamiltonian) and shift operators (that c onnect eigenfunctions of different Hamiltonians inside the factorizati on hierarchy). The operators appearing in the factorizations span a dy namical algebra whose action is schematically drawn on a two-dimension al lattice. Afterwards it is shown in detail that the relevant subalge bra is isomorphic to an extended (1 + 2) Newton-Hooke conformal algebr a corresponding to a two-dimensional wave equation. As a byproduct; fo r each element of the hierarchy there is derived a new one-parametric continuous family of almost-isospectral radial Hamiltonians. (C) 1996 Academic Press, Inc.