1) (25 points) A particle of mass m is scattered by a symmetric square well potential given by V(a) = -Vo lac) 0 |ac| > a/2 (1) The incoming and outgoing plane waves of even and odd parity are It (k; x) = e iklx] I_ (k; x) = sign(x) e-ikz] (2) O+ ( k ; 2 ) = etiklal O_(k; x) = -sign(x) etiklol (3) The corresponding scattering states for (x| > a/2 are 7 + ( k; 2) = It (k; x) + S+ + (k)0+ (k; 2) (4 ) _ (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