WKB expansion for the angular momentum and the Kepler problem: From the torus quantization to the exact one

We calculate the WKB series for the angular momentum and the non-relativistic three-dimesional 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.