= Two-term Dirichlet WKB quantization
{title2=$\epsilon^{-1}\int_a^b K\,dx+\epsilon\int_a^b\sigma_1\,dx=n\pi+O(\epsilon^3)$}
For smooth positive $K$ on an interval with regular Dirichlet <boundary conditions>, there is no turning-point phase shift. Combining conjugate <WKB approximation> branches to vanish at the first endpoint makes the total phase at the second an integer multiple of $\pi$. The first correction is the integrated <WKB phase correction for a slowly varying oscillator>. For $K=x+1$ on $[0,1]$ the resulting <eigenvalues> are $4\pi^2n^2/9-3/16+O(n^{-2})$.
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