(a) Take the particle-in-the-box wave functions 1/2 4, (x) = sin a and energies En nh = 8ma take a 8x10-11 meters take the mass m = 9.1 x 10-31 kg Consider the time dependent wave packet probability density for a superposition of n=1, n=2, n=3, each with equal amplitude coefficients, c = c2 = C3 = 1. In other words, take 3 y(x,t) = (x)eit/h 24, n=1 First multiply everything out to find 4*(x) (x) at various times. Parts of the multiplication will look constant and parts will be oscillatory. Put the oscillatory parts into a usable cos(Awt) form and be sure to retain all the parts in x. Recall that expressions containing En can be converted to frequencies on. (b) What are the values of A@12, A@23, A@13 in cm? (c) Now use a computer and an Excel spreadsheet program or similar method to graph a "movie" of the time dependent wave packet motion of the particle in a box versus both x and t. Decide whether to use radians or degrees and select appropriate intervals of linear time to display the oscillatory part. The goal is to show 4* (x) 4(x) versus x and t (3D plot) at enough time delays in sequence to visualize the wave packet motion.