4. Delta function well scattering Instead of sending a particle from innity with well-dened momentum p, suppose we had a Gaussian wavepacket, with some small momentum uncertainty 0,, (i.e. large position uncertainty 01.), with mean momentum p and mean position d (with d > am, so it's on the left of the well). (a) What is the probability that after a very long time, the particle remains near a: = 0? (You may leave your answer as an integral.) (Hint: which energy eigenstates are localised?) (b) If this probability is not zero, comment on the apparent contradiction between R + T = 1 and your result. (Hint: what happens to this probability as we take d > 00 or up > 0?)