Chapter 18 Lab

1. First, the left graph shows the energies of the system: blue=potential while red=particle's energy. You can drag the red energy bar up and down with your mouse. Click the "Solve" button at the lower right to see that the energy solution (technically, the eigenvalue) is ~-0.1895. Why do you think this is the solution and the other energy values are not? What is special about the right graph for this particular energy value? The correct answer to this question impacts your ability to "get" the rest of the questions.
2. The right graph shows psi, the wave function, either squared or not. Note the effect of clicking the "psi squared" checkbox. In what sense is the checkbox "backwards?"
3. Adjust the width of the potential well from 1 to 4. Can you find both solutions? What are the corresponding energies?
4. Now adjust the depth of the well to 4 as well as a width of 4. How many solutions are there now? What are the corresponding energy eigenvalues?
5. Now adjust the depth of the well to 8 (leave width=4). How many solutions are there now?
6. What trend do you detect?
7. Click on the lower-left button so that it changes to "Quadratic" potential. This is a decent model of a diatomic molecule like hydrogen H₂, nitrogen N₂, or oxygen, O₂. Note that regardless of the textbox settings, this well is 6 units deep and 10 wide. How many energy energy eigenvalues are there?
8. How are the "Quadratic" potential waves similar to the square well waves?
9. How are the "Quadratic" potential waves different from the square well waves?