Quantum Mechanics - Theory of Scattering : Born Approximation
The method of partial waves is limited to the case of low-energy scattering by short-range central potentials. If the potential is not necessarily central and energy is high then the scattering problem is solved by an approximate method,known as Born Approximation. If the interaction is weak,so that the scattered wave is not large then it is expected that the Neumann series will converge rapidly and the first term in the series provides an approximation to the wave function. This is what we call First Born Approximation. The condition for the validity of Born approximation has been also discussed. The required condition for the validity of Born approximation is that the scattered wave should be much smaller than the incident wave.