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The deuteron theory is renewed and completed for non-local Hamiltonians. A method to calculate deuteron wave functions is given. The formula for the current density and the magnetic dipole moment of a non-local potential is derived, and applied to the GCT, GT, and HJ-potential. The effects of a unitary transformation on the deuteron data — electric quadrupole moment, magnetic dipole moment, and radius — are shown. For the numerical calculations the Ristig-Kistler transformation and the HJ-potential were used. It is shown that an overall fit cannot be reached.