PHY 6646
K. Ingersent
Information Concerning Mid-Term Exam 1
The first mid-term exam will be held from 10:35 to 11:35 p.m. on Friday, February 22 in
NPB 1101. (Note: The exam will begin five minutes before the usual starting time for the
class and will end five minutes later.)
The exam will cover all material discussed in the course up to and excluding the topic
of Brillouin-Wigner perturbation theory. A list of topics, cross referenced to the course texts,
appears on the Web at www.phys.ufl.edu/∼kevin/teaching/6646/02spring/topics.html. (Note
that we have skipped entirely Shankar’s lengthy discussion of the connection between the
WKB approximation and the path integral formulation of quantum mechanics. Also, the
exam will not cover the various techniques discussed in Shankar Section 17.2 to evaluate the
sum over states in the second-order energy correction.)
You will be allowed to consult Shankar, your lecture notes, and homework solutions
(yours or mine). No other written/printed materials will be allowed.
The exam will likely consist of two questions, of roughly equal weight. Each question
may deal with more than one of the topics we have covered in the course. (For instance, one
question might involve a variational treatment of a particle in a uniform electric field.)
The questions will test your ability to apply the concepts covered in the course to unfamiliar situations. Calculations will be involved, but these will be designed to be much less
laborious than the ones assigned for homework.
The following question may be good practice for the exam:
1. Shankar Exercises 14.4.1 and 14.4.6.
2. Shankar Exercises 16.1.1, 16.1.2, and 16.1.3.
3. Consider the particle-in-a-box problem corresponding to the potential
(
V (x) =
0
+∞
for |x| < a/2
for |x| ≥ a/2.
Now suppose that we add a delta-function perturbation
H1 = V1 δ(x).
(a) Find the first-order shift in the stationary state energies.
(b) Find the second-order shifts. (You should be able to carry out the sum over states
explicitly for this problem, although you probably wouldn’t be expected to do so
in an exam.)
4. Shankar Exercise 17.3.2.