Potential Scattering

We want to consider the scattering of particles by a fixed short-ranged potential; this excludes the case of a Coulomb potential, which requires separate treatment. Suppose, as in Fig. 9-1, that the source of particles is located far to the left of the target, and that a particle emitted by the source at early time t₀ is in a wave packet state (9-1) https://www.w3.org/1998/Math/MathML"> ψ ( r ,   t 0 )   =   ∫ d 3 k ( 2 π ) 3   e i k ⋅ r   a k . https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429499265/ff9ae276-bf0f-4700-9154-eaa3ea82fbc6/content/eq1089.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Fig. 9-1 Wave packet of average momentum ħ<bold>k</bold> ₀ incident on a target. https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429499265/ff9ae276-bf0f-4700-9154-eaa3ea82fbc6/content/fig9_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>