Abstract
It is shown explicitly, in the framework of the Klein-Gordon equation, that the algebraic method based upon unitary irreducible representations of the group SO(2,1) used to solve the problem of strong Coulomb coupling (e2Z>l+1/2) is equivalent to constructing solutions that are orthogonal with respect to some mixed scalar product, rather than the standard Klein-Gordon scalar product. This elucidates the difference between the spectra given by Case's method (1950) and by the algebraic method. By explicitly computing scattering states, it is further shown that algebraic solutions describe absorption of the particle as in the corresponding classical problem.
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