M 311 Spring 2004
HOMEWORK SUMMARY REPORT
Chapter number: 8
Section number: 2
Exercise number: 4
Number of papers received: 5
Reviewing committee: epsilon
List all participating committee members:
c-glaser,j-bosshard
Author(s) of paper(s) chosen for publication: a-coots
Comments: We chose Amanda's paper, because of the depth of its
explanations as well as its taking into account the b=0 case. All other
papers are correct when b is not equal to zero.
GRADER'S COMMENT: Nobody made the interesting observation that the
eigenbasis is independent of b (except for the freedom to choose a
different one when b = 0).
INSTRUCTOR'S COMMENT: This exercise gives away the teacher's secret
weapon for finding an exam problem that is easily solvable and is
guaranteed to have a degenerate (multiple) eigenvalue. Whenever all the
diagonal elements are equal and all the off-diagonal elements are equal to
something else, (1,1,...,1) is always a nondegenerate eigenvector and
all the vectors orthogonal to it are eigenvectors of the second
eigenvalue. In nuclear physics the (1,1,...,1) solution is called the
"giant dipole resonance".