High order WKB approximation and singular perturbation theory
Date: July 18th (Thursday)
Time: 09:20-09:45
Abstract
In the first part high order WKB quantization formulas
for one-dimensional systems are derived by alternating
repeated automatic partial integration with respect to x
and V'(x). At the end nonintegrable singularities are
rewritten as multipe energy derivatives to allow numerical
treatment of the integrals.
The second part discusses the second order dependence of
the eigenvalues of a finite quantum well in an electric
field. Because the system has a continous energy spectrum,
classical perturbation theory yields untractable
integrals. Starting from the exact solution a singular
perturbation theory is performed to yield relatively
simple closed form expressions for all eigenvalues.
