October 27 Kerchof 326, 3:30 pm.
L. Thomas
"On the Schrodinger operator for a special wire loop configuration"
We continue discussion concerning the Schrodinger operator
H= -d^2/ds^2+k^2(s), with the potential k^2(s) the square of the
curvature k(s) along a loop of length 2\pi. Again, we consider the
conjecture that H\geq 1. We show this is so for wire configurations
close to a particular family of singular "squashed" loops. An
integrable Schrodinger operator arises, diagonalized by Gegenbauer
polynomials.