A Momentum Transformation Connecting a NN Potential in the Nonrelativistic and the Relativistic Two-Nucleon Schroedinger Equation

An analytical relation between center of mass momenta in a nonrelativistic and a relativistic two-nucleon Schr\"odinger equation is proposed which allows to analytically rewrite 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.