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The non-relativistic energy levels of ortho-positronium are calculated in thequadrupole and octupole approximations for the interaction potential. For thispurpose, the RST eigenvalue problem of angular momentum is illustrativelysolved for the quantum numbers $\jO=0,1,2,3,4$ and $\bjz=\pm 1$. Thiseigenvalue problem admits \emph{ambiguous} solutions for $0<|\bjz|<\jO$ whereasthe solutions for $\bjz=0$ and $\bjz=\pm \jO$ are \emph{unique}. In order toattain some (at least approximative) solutions of the energy eigenvalue problemone tries a factorized ansatz for the wave function and thus splits off theangular problem (with its ambiguous solutions) from the residual radialproblem. The latter does, as usual, finally fix the energy eigenvalues. But itis just by this procedure that the ambiguity of the angular problem istransferred to most of the energy levels which thereby become doubled. Thecorresponding doubling energy amounts to (roughly) one percent of the totalbinding energy and is, however, of purely \emph{electric} origin, sincemagnetism is completely neglected. Indeed, the charge distributions of bothpositronium constituents (i.e.\ electron and positron) do inherit theirambiguity from the ambiguous solution of the angular eigenvalue problem($\leadsto$ charge "dimorphism"); and naturally the dimorphic configurationsmust then possess slightly different interaction energies of the electrostatictype.

Dimorphism of Ortho-Positronium in Relativistic Schr\"odinger Theory