M. Robnik et L. Salasnich, WKB EXPANSION FOR THE ANGULAR-MOMENTUM AND THE KEPLER-PROBLEM - FROM THE TORUS QUANTIZATION TO THE EXACT ONE, Journal of physics. A, mathematical and general, 30(5), 1997, pp. 1719-1729
We calculate the WKB series for the angular momentum and the non-relat
ivistic three-dimesional Kepler problem. This is the first semiclassic
al 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 quant
ization of the angular momentum and of the radial Kepler problem separ
ately 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.