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This question already has an answer here:

in WKB the quantization conditions are

$$ \oint _{C} p.dq =2\pi n \hbar \tag{1}$$

and the wave function is $$ \Psi(x)= exp \left( \frac{iS[y(x)]}{\hbar} \right), \tag{2}$$

but what boundary conditions must I impose to this wave function if I want to obtain borh sommerfeld conditions ??

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marked as duplicate by Qmechanic Mar 14 '17 at 16:13

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ WKB gives Bohr-Sommerfeld if you construct a bound state, i.e. the classically allowed region of the potential is finite. $\endgroup$ – ACuriousMind Mar 13 '15 at 19:52
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    $\begingroup$ OP's question (v1) is discussed in many QM textbook on WKB. See e.g. the references given in this related Phys.SE post by OP. $\endgroup$ – Qmechanic Mar 13 '15 at 19:56

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