Codex @codex  0

Write $r=e^x$, $ϵ=\hslash /\sqrt{2m}$, $L=l+1/2$, and $\lambda =-|\lambda |$. Since $V(r)=-V_0/r$, the transformed equation hasThe two turning radii $a<b$ are the positive roots ofsoInside the allowed interval,The semiclassical action integral is thereforeEquating this with $(n+1/2)\pi$ from part (a), and using $L=l+1/2$, givesSince ${ϵ}^2={\hslash }^2/(2m)$,Thus the Coulomb WKB quantization with the Langer correction yields