Marko Robnik, Luca Salasnich
WKB expansion for the angular momentum and the Kepler problem:
from the torus quantization to the exact one
(29K, LaTeX)
ABSTRACT. We calculate the WKB series for the
angular momentum and the non--relativistic 3-dim Kepler problem.
This is the first semiclassical treatment of the angular
momentum for terms beyond the leading WKB approximation.
We explain why the torus quantization (the leading WKB term)
of the full problem is exact, even if the individual torus
quantization of the angular momentum and of the radial Kepler
problem separately is not exact. In this way we derive Langer's rule,
calculate the first correction to the leading Langer's term and
conjecture the form of all higher terms.
(J. Phys. A: Math. Gen. 30, 1719-1729 (1997))