H133: 1094 Session 5

Write your name and answers on this sheet and hand it in at the end.
After the indicated time, move on to the next activity, even if you are not finished!

1. Q10: The Schrodinger Equation [20 min.]

In chapter Q10, we motivate the Schrodinger equation (Q10.12). Here we consider some basic problems from the chapter.

1. Answer two-minute question Q10T.4.
   
   
   
   
   
   
2. How can we test if a given wave function psi(x) is a solution to the Schrodinger equation? [See Section Q10.4 and equation (Q10.14).]
   
   
   
   
   
   
3. Do problem Q10S.1, showing that b = sqrt[2m(E-V0)]/hbar. [Note the hint.] Is b real?
   
   
   
   
   
   
   
   
   
   
4. Do problem Q10S.3. [Note the hint.] Make sure that your answer for b is a real number when E<V0.
   
   
   
   
   
   
   
   
   
   
5. Why must a physically acceptable wave function go to zero as x goes to plus or minus infinity?
   
   
   
   
   
   
6. What happens in SchroSolver if you choose an energy that is not an energy eigenvalue? How can you use this to zero in on the correct eigenvalue? Try out your method.
   
   
   
   
   
   

2. Q11: Wavefunctionology [25 minutes]

Do the "Wavefunctionology Exercises" worksheet and hand it in together with this sheet. Below we give some suggestions and hints for each part.

Part 1.

1. There is one error for two of the wave functions and two errors for each of the other two.
2. To be systematic, consider each of possibilities B through F in turn.
3. Each of the incorrect possibilities corresponds to one of the "Rules for Sketching Wavefunctions", which are labeled 1 through 6 (see handout). B goes with rule 1, C goes with rule 6, D goes with rule 3, E and F both go with rule 2, and G goes with rule 4 or rule 5.

Part 2.

1. First decide how many bumps there should be.
2. Then mark where the wave function is wavelike and where it is exponential-like.
3. Finally, where will the amplitude be large and small?
4. Draw a smooth wave function with these features.
5. Use the PhET applet "Quantum Bound States" or SchroSolver to check your answer.

Part 3.

1. Follow the same steps as in Part 2.
2. Use the SchroSolver to check your answer.

Part 4.

1. Follow the same steps as in Part 2.
2. Use the SchroSolver to check your answer.