An analytical relation between center of mass momenta in a nonrelativistic and a relativistic two-nucleon Schr\"odinger equation is proposed which allows analytically rewriting the two Schr\"odinger equations into each other. As a consequence a NN potential occurring in the relativistic Schr\"odinger equation can be gained from a nonrelativistic one by an analytical procedure. The S matrices in the two equations are exactly identical, and therefore the two-nucleon phase shifts are also.
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