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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.

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The Green's functions for charged particles of spin zero and 1/2, which are subjected to the action of the field of an electromagnetic plane wave, are calculated in the path integral formalism. It is also shown that in the case of spin 0, the semi-classical Green's function obtained via a canonical transformation, is accurate. These Green's functions are obtained under a compact form. The waves in the case of spin 0 and the wave functions in the case of spin 1/2 are then deduced.