Show all of your work and drawings. Explain.

4. (5 points) Using your knowledge of perturbation theory, predict the changes in the wave function and energies for the following modified particle-in-a-box systems with the given wave function y; in the figures. Compute a number for the energies and compare it to the original energy, but just sketch the perturbed wave functions and show the changes. (f) 1 is the n = 1 Vi = v1 particle-in-a-box wave function. 0 0 -5 L/2 L (g) 1/2 is the n = 2 Wi = 1/2 particle-in-a-box wave function. U -5- L/2