1) (25 points) A particle of mass m is scattered by a symmetric square well potential given by -Vo V(x) = |ac| 0 120| > a/2 (1) The incoming and outgoing plane waves of even and odd parity are It ( k ; 20 ) = e-iklz1 I_ (k; x) = sign(x) e-ik(x] (2) O+ ( k; 2) = etiklal O_ (k; x) = -sign(x) etikz] (3) The corresponding scattering states for (x| > a/2 are a/ + ( k; 2) = It (k; I) + s+ + (k)0+(k; z) (4) 2_ (k; x) = I_ (k; x) + S_ _ (k)O_(k; x) G where S+ + and S__ are the diagonal elements of the S matrix in parity ba- sis. Calculate S++ and S_- and the corresponding transition /reflections coef- ficients. Use the notation q2 = k2 + Uo, Uo = 2mVo/h. Interpret the poles and zeros of S+ + and S__ in terms of bound states