  We will prove a general approximate quantization rule $%
\int_{L_{E}}^{R_{E}}k_0$ $dx=(N+\frac{1}{2})\pi $ for the bound states in the
potential well of the equations $e^{-i\pi n/2}\nabla_x ^{^{n}}\Psi =[E-\Delta
(x)]\Psi ,$ where $k_0=(E-\Delta )^{1/n}$ with $N\in\mathbb{N}_{0} $, $n$ is an
even natural number, and $L_{E}$ and $R_{E}$ the boundary points between the
classically forbidden regions and the allowed region. The only hypothesis is
that all exponentially growing components are negligible, which is appropriate
for not narrow wells. Applications including the Schr\"{o}dinger equation and
Bogoliubov-de Gennes equation will be discussed.
