1. Show that our traveling wave equation from earlier chapters is a solution to the classical wave equation.[br]2. Solve for the energies of an electron confined to a linear region of length L=0.4 anstroms.[br]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?[br]4. Given the probability density for the particle in a box, how will it look as [math]n\longrightarrow\infty[/math]? The [i]correspondence principal[/i] 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?[br]5. What is the average position of the particle in a box of width L?[br]6. What is the average momentum of the particle in a box of width L?[br]7. What are the energies of the particle in a box in relation to the wave number? [br]8. What is the vibrational absorption frequency of a diatomic oxygen molecule? It's elastic constant is k and each atom has a mass [math]m_o.[/math]

[list=1][*]Plug it in like we did in class.  [/*][*][math]E_n=\frac{h^2n^2}{8mL^2}[/math], but know how to find these energies.[/*][*][math]\approx1.46\%\text{;}8.5\%[/math][/*][*]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.[/*][*][math]E_n=\frac{\hbar^2k^2}{2m}[/math][/*][*][math]f=\hbar\sqrt{\tfrac{2k}{m_o}}[/math][br][/*][/list]