Consider a neutron which is confined to an infinite potential well of width a = 8fm. At time t = 0 the neutron is assumed to be in the state

2x sin sin 7a 2 Y(x,0): = V sin 7a 7a (a) If an energy measurement is carried out on the system, what are the values that will be found for the energy and with what probabilities? Express your answer in MeV (the mass of the neutron is mc2 - 939 Me V, hc 197 MeV fm). (b) If this measurement is repeated on many identical systems, what is the average value of the energy that will be found? Again, express your answer in MeV. (c) Using the uncertainty principle, estimate the order of magnitude of the neutron's speed in this well as a function of the speed of light c.