17.7. Scattering in a potential with two delta functions Consider a one-dimensional system of quantum mechanics with Hamiltonian given by H = p2 2m

+V(x)

with V(x) = −g1 δ(x+a)−g2 δ(x+a)

(g1 and g2 positive).

a. Compute the phase shifts δ0 and δ1 and the corresponding S-matrix elements.

b. Analyse the analytic structure of the S-matrix by varying the momentum k.

c. Determine the wave function of the bound states.