\[\Phi(r) = A e^{i k \cdot r}+\int G \left(r-r^{\prime} \right) U \left(r^{\prime} \right) A e^{i k \cdot r^{\prime}} d^{3} r^{\prime}+\iint G \left(r-r^{\prime} \right) U \left(r^{\prime} \right) G \...\[\Phi(r) = A e^{i k \cdot r}+\int G \left(r-r^{\prime} \right) U \left(r^{\prime} \right) A e^{i k \cdot r^{\prime}} d^{3} r^{\prime}+\iint G \left(r-r^{\prime} \right) U \left(r^{\prime} \right) G \left(r^{\prime}-r^{\prime \prime} \right) U \left(r^{\prime \prime} \right) \Phi \left(r^{\prime \prime} \right) d^{3} r^{\prime} d^{3} r^{\prime \prime} \nonumber\]
The scattering amplitude f(Ω) can be calculated using a variety of analytical and numerical methods. We will discuss one particularly important approach, based on a quantum variant of the Green’s fu...The scattering amplitude f(Ω) can be calculated using a variety of analytical and numerical methods. We will discuss one particularly important approach, based on a quantum variant of the Green’s function technique for solving inhomogenous differential equations.
