Partial wave dispersion relations are used as dynamical equations describing nucleon-nucleon scattering. For each state, from the empirical values of the phase shifts for different relative energies of the two nucleons, the first term of the Born series is obtained. In this connection, approximate methods of solving the inverse of a dispersion relation are discussed, and the results are compared with those obtained from the Schrödinger equation. Off-diagonal elements of the Born term for energy non-conserving processes are found by extrapolating the diagonal elements. The matrix obtained in this way enables one to calculate the reaction matrix and also the harmonic oscillator matrix elements directly from the phase shifts. Numerical results for both types of calculation are presented and compared with recent works of Elliott and collaborators.