Question #3 (Particles in a box, 35 points) One thousand particles (mass m) are confined in a one-dimensional box with walls at x=0 and x=L. At 1=0, the state of each particle is w(x,t=0) = Ax(x-L). a) Normalize w(x,t=0) and find the constant A. [5 pts] b) How many particles are likely to be found in the interval between x=0 and x =L/2 at t=0? [7.5 pts] c) How many particles are likely to be found in the interval between x=L/2 and x =L at t=0? [7.5 pts] d) How many particles are likely to have an energy corresponding to the n=5 energy eigenstate at t=0? [5 pts]