where f is the scattering amplitude. According to the probability interpretation of quantum mechanics the differential cross section is given by d σ σ / d Ω Ω = | f ( θ θ ) | 2 (the probability per unit time to scatter into the direction k ). If we consider only s-wave scattering the differential cross section does not depend on the angle θ θ , and the total scattering cross section is just σ σ = 4 π π | f | 2 . The s-wave part of the wavefunction ψ ψ ( r , θ θ ) is projected out by using the standard expansion of a plane wave in terms of spherical waves and Legendre polynomials P l ( cos ⁡ ⁡ θ θ ) :