PROBLEMS
1. Show that our traveling wave equation from earlier chapters is a solution to the classical wave equation.
2. Solve for the energies of an electron confined to a linear region of length L=0.4 anstroms.
3. What is the probability of finding an electron in the ground state between 0.10 L and 0.15 L in a box of width L? What is the probability in the n=3 state?
4. Given the probability density for the particle in a box, how will it look as ? The correspondence principal states that as the quantum number goes infinite, the behavior should appear classical. What is the probability of finding such a classical particle in a small section of the box of width L/10, for instance?
5. What is the average position of the particle in a box of width L?
6. What is the average momentum of the particle in a box of width L?
7. What are the energies of the particle in a box in relation to the wave number?
8. What is the vibrational absorption frequency of a diatomic oxygen molecule? It's elastic constant is k and each atom has a mass
ANSWERS
- Plug it in like we did in class.
- , but know how to find these energies.
- The probability to find the particle in any small region of width dx=finite will be the same everywhere inside the box as one would expect in the macroscopic realm.
- L/2
- don't worry about this one. didn't discuss the momentum operator.