Question 01 - Separable potential scattering Consider a potential that can be written as: V = Abold. with (xx) = 1, - and [x). some state vector in Hilbert space. This type of potential is called separable. a) Show that: LIG. (E)T* (8) = (X(IG.(E)bx))-1 - 1 use this result to get the matrix T exactly. bj Consider that, for a given B . 83/2 g(p) = 1 7 32 +p2 d) Considering that k cot(60(k)), , calculate , obtain the effective range of a. e) Calculate A " for the previous example considering that the system has an bond state of energy EB When B 4 0, what is the effective range value? Discuss the physical meaning of the result you found out