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High order WKB approximation and singular perturbation
                             theory
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Michael Trott

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Date:  July 18th (Thursday)\\
Time:  09:20-09:45\\

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Abstract
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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.

