  Weak magnetic monopoles with a continuum of charges less than the minimum
implied by Dirac's quantization condition may be possible in non-associative
quantum mechanics. If a weakly magnetically charged proton in a hydrogen atom
perturbs the standard energy spectrum only slightly, magnetic charges could
have escaped detection. Testing this hypothesis requires entirely new methods
to compute energy spectra in non-associative quantum mechanics. Such methods
are presented here, and evaluated for upper bounds on the magnetic charge of
elementary particles.
