An Interdisciplinary Journal

* 2000, Volume 3, Number 3, pp.214--219*

We obtain the rigorous WKB expansion to all orders for the radial
Kepler problem, using the residue calculus in evaluating the WKB
quantization condition in terms of a complex contour integral in the
complexified coordinate plane. The procedure yields the exact energy
spectrum of this Schrödinger eigenvalue problem and thus resolves the
controversies around the so-called "Langer correction". The problem is
nontrivial also because there are only a few systems for which all orders
of the WKB series can be calculated, yielding a convergent series whose sum
is equal to the exact result, and thus sheds new light to similar and more
difficult problems.

*Key words: *radial Kepler problem, WKB expansion, Schrödinger
eigenvalue problem.

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Last updated: *June 19, 2001*