Show that at low energies (ka→0) the requirement (13.48) for the validity of the Born approximation becomes
ℏ2k2μ∫0∞dr′V(r′)kr′∼ℏ2μV0a2≪1
where V0 is the order of magnitude of the potential energy, a is the range of the potential, and we have neglected constants of order unity. By comparing this result with (13.49), argue that if the Born approximation is valid at low energies, it works at high energies as well.