  In this article, we propose a numerical approach to solve quantum mechanical
scattering problems, using phase function method, by considering neutron-proton
interaction as an example. The nonlinear phase equation, obtained from the
time-independent Schrodinger equation, is solved using the Runge-Kutta method
for obtaining S-wave scattering phase shifts for neutron-proton interaction
modeled using Yukawa and Malfliet-Tjon potentials. While scattering phase
shifts of S-states using Yukawa match with experimental data for only lower
energies of 50 MeV, Malfliet-Tjon potential with repulsive term gives very good
accuracy for all available energies up to 350 MeV. Utilizing these S-wave
scattering phase shifts, low energy scattering parameters, and total S-wave
cross section have been calculated and found to be consistent with experimental
results. This simulation methodology can be easily extended to study scattering
phenomenon using phase wave analysis approach in the realms of atomic,
molecular, and nuclear physics.
