Scattering off a delta function and a wall. 19 pollits] Consider our usual one-dimensional potential with V(x) = co for a 0 1>0. We scatter particles with mass m and energy E > 0 off this potential. We have 2m Ea2 (ka)2 mag unit free. planckover2pil planckover2pil (a) Calculate the phase shift 6(k). Write the answer in the form sin? (ka) tand = h(ka; A) where h(ko; A) is a function you must determine. Explain how, with 6 known, one readily finds the amplitude A(k) multiplying the 'sin' function in the wave- function for 0 co? (c) Plot 6, the time delay Ids, and | A) as functions of ka e [0, 10] for A = 5. Do you see resonances? If so, identify the values of ka, the time delay 1ds and the magnitude of A). Is the plot of & consistent with Levinson's theorem? a dy