Representation theory of so(4,2) for the perturbation treatment of hydrogenic‐type hamiltonians by algebraic methods

The representations of so (4,2) which are applicable to the perturbation treatment of one‐electron Hamiltonians of the form H = H 0 + λ V are discussed, where H 0 is a hydrogenic Hamiltonian. A unified construction of the representations of so (2,1) and so (3) is outlined and the representations of so (4) [and also so (3,1)] are then obtained using both the vector operator method and angular momentum recoupling techniques. The merging of so (2,1) and so (4) then leads in a natural way to so (4,2). An outline of perturbation theory applications such as the Stark and Zeeman effects is also given.