Asymptotic behavior of the spectrum of an anharmonic oscillator

The asymptotic expansion
$$ \lambda_n=n-\frac{1}{2}+\frac{1}{2\pi\sqrt n}\biggl[\int_{-\infty}^{\infty}q(t)d(t)+o(1)\biggr], \quad n\to\infty, $$
is obtained for the spectrum of the equation $-y^{''}+[x^2/4+q(x)]y=\lambda y$, $-\infty<x<\infty$, of the anharmonic oscillator. The ease when the potential $v(x)$ has the form $v(x)=\alpha|x|+q(x)$ is also considered.