I discuss the advantages and disadvantages of several procedures, some known and some new, for constructing stationary states within the mean field approximation for a system with pairing correlations and unequal numbers spin-up and spin-down fermions, using the two chemical potentials framework. One procedure in particular appears to have significant physics advantages over previously suggested in the literature computational frameworks. Moreover, this framework is applicable to study strongly polarized superfluid fermion systems with arbitrarily large polarizations and with arbitrary total particle numbers. These methods are equally applicable to normal systems.
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