Deforming SO(4,2) generators

Abstract

The energy spectrum and degeneracy of a Hamiltonian can be studied using either the theory of special functions or spectrum generating algebras. In this thesis the second approach is used for the analysis of the H-atom Hamiltonian. SO(2,1) provides the spectrum generating algebra for the H-atom problem. The geometrical symmetry group SO(3) was rst generalized to SO(4), the degeneracy group, then merging it with SO(2,1), the dynamical group SO(4,2) was obtained. The ladder operators of SO(4,2) connect all the states of the H-atom. In the past, the generators of the SO(2,1) group were generalized by the point transformation r -G(r)^r then these generators are deformed by the variation G(r) - G(r) + g(r). This formalism has led to a perturbation method. In this work the historical development of above formalism is traced and the 15 generators of the SO(4,2) group are deformed.