It is not before towards the end of the century that Wintgen, Richter and Tanner nevertheless submit a (semiclassical) quantization of that kind for the Helium atom - and thus refer indirectly to Poincaré, too.

It seems that the dominance of quantum theory in physics has hindered in fact a deeper understanding of deterministic dynamical systems (chaos theory) for decades - and rendered to itself bad service this way. For a successful semiclassical quantization just a detailed knowledge of the corresponding classical behaviour turns out to be necessary.