Abstract: In this study, the radial Schrodinger equation for central coulomb potential using numerical Runge-Kutta has been solved. Energy eigenvalues for hydrogen and positronium bound systems is derived -13.6056 and -6.803 eV, respectively. Numerical results of ground state modes of wave functions for hydrogen and positronium R (r) and the presence probability function |rR(r)|2has been presented. These results are in good agreement with analytical calculations of the hydrogen atom in modern physics and quantum mechanics. Therefore, numerical methods can be very useful and effective in solving physical problems.