The final exams have been graded and placed in campus mailboxes for grads in Physics, Applied Physics, and Astronomy. All other
students may pick up their exams at 524 Clark Hall. As explained on the course information page, course grades are based on an equally
weighted combination of the homework and final exam scores (we also dropped the lowest homework score). Best wishes for the holidays!
Some random items regarding the exam:
For the special case E_1 = E_2, in problem 2 (c), the location of the equilibrium point does not depend on
the magnitude of the electric field (that's what makes the math easier).
In 2(a) the "limit of very small t" is not the same as "t = 0" ! Your sketch should reflect this fact.
When sketching the energy levels in problem 2(a) you are better off working with H directly (in the limit of very small t),
rather than the analytic formulas for the eigenvalues (that you are also asked to derive).
In problem 1 you should not be solving for radial wavefunctions. When using the "flat earth approximation" the radial
wavefunctions are essentially the same as the wavefunctions for the 1D problem in homework assignment 5.
If the matrix element integral in problem 3 is giving you trouble, consider not doing the electric dipole
transformation trick (take the expectation value of p directly).
In problem 2 the molecule is enormous and should always be treated classically. In part (d) the angle theta
is still a classical variable, and varies linearly with time (making the electron Hamiltonian time-dependent).
sin(2x) = 2 sin(x) cos(x)
Here is the take-home final exam (instructions on first page). The due date is Thursday, December 6, 4 pm.
Place your exam in the physics office collection box marked "Physics 572".
Your graded homework 12 will be delivered to your mailbox (physics grads), or available outside 524 Clark, by Monday noon.
