1. Show by example that yn ym are orthognal. (Hint: Use the Table command.) You can also try
to show this for all m and n.
2. Calculate <p>, <x>, s p 2 , and sx 2 for a particle in a box.
3. Calculate sx s p and show what it is equal to when n=1.
4. Use Plot3D to show what the wavefunctions look like for a particle in a 2D box. Are there any
degenerate states. (Hint: Make a Table of plots with n and m ranging up to about 3.)
5. Plot the first 3 y2 and y for a particle in a 1D box in seperate plots. Put both the wavefunction
and probability distribution on one plot, coloring the two fnuctions differently. Do the extrema
of y correlate with the extrama of y2 ? What about the nodes in y?