I think it’s instructive to distinguish quasi-particle and particle quantum numbers in the same bound system. I submitted a short note about it at http://www.science20.com/qed_reformulation_feasible/blog/unknown_physics_particle_orbital_momentum.
Also I discussed this question in the Lubosh Motl’s blog: http://motls.blogspot.com/2011/01/twistor-minirevolution-goes-on.html, in the comment section, without success, though.
The intriguing part is that any particle orbital momentum 
or 
in a two-particle bound system (atom, positronium, etc.) has seemingly quantized, but generally non-integer eigenvalues (certain fractions of 
), unlike the integer quasi-particle one 
. Normally people object to this simple result, but without right grounds because the rule of addition of independent angular momenta is not applicable to the strongly correlated system. I thought the “main” operator was and the particle ones were just functions of it. In fact, I admitted an error. Briefly: apart from a fraction of , each particle orbital momentum 
contains a fluctuating addendum, so non-integer are the particle expectation values, not their eigenvalues. The latter do not exist since the bound particles are always in mixed states.
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