Algebraic treatment of a general noncentral potential

Abstract

It is shown that the problem of a particle moving in a noncentral potential generalizing the Coulomb potential and the Hartmann ring-shaped potential accepts SO(2,1)⊗SO(2,1) as a dynamical group, within the framework of the Kustaanheimo–Stiefel transformation. The Green’s function relative to this compound potential is calculated through the algebraic approach so(2,1) and with the help of the Baker–Campbell–Hausdorff formulas. The energy spectrum and the normalized wave functions of the bound states can then be deduced. Eventually, the Coulomb potential, the Hartmann ring-shaped potential and also, due to its close link with the latter, the compound Coulomb plus Aharonov–Bohm potential may all be considered as particular cases.