Suppose we are given an ODE problem $$ y''(x)+V(x)f(x)=E_{n} y(x) $$ with boundary conditions $ y(0)=y(\infty)=0$. Here $V(x)$ is a potential function.
Then is it always true that (for $n \gg 1$) $$ E_{n}^{\rm WKB} \sim E_{n} $$
where WKB means the eigenvalues evaluated via the WKB approach?
