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Couchyam

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- TL;DR Summary
- Can the Bohr-Sommerfeld approach be adapted to handle quasi-periodicity? (Or would that just be another special case of the WKB approximation?)

Recall that in the semi-classical Bohr-Sommerfeld quantization scheme from the early days of quantum mechanics, bound orbits were quantized according to the value of the action integral around a single loop of a closed path. Clearly this only makes sense if the orbits in question permit closed paths, however, which is not always the case (consider for example a central potential of the form ##1/r^{1+\epsilon}##, ##\epsilon \neq 0##, in which orbits are generically (in ##\epsilon## as well as initial conditions) quasi-periodic in ##\theta(t)## and ##r(t)##. Quasiperiodicity presumably would have been a well-understood (dare I say pedestrian) concept in Bohr's time, and so it must have been considered to some extent. Did Bohr and/or Sommerfeld write anything about this? If not, how might their approach be expanded on to incorporate quasiperiodicity?