  The aim of this work is to provide an upper bound on the eigenvalues counting
function $N(\mathbb{R}^n,-\Delta+V,e)$ of a Sch\"odinger operator $-\Delta +V$
on $\mathbb{R}^n$ corresponding to a potential $V\in
L^{\frac{n}{2}+\varepsilon}(\mathbb{R}^n,dx)$, in terms of the sum of the
eigenvalues counting function of the Dirichlet integral $\mathcal{D}$ with
Dirichlet boundary conditions on the subpotential domain $\{V< e\}$, endowed
with weighted Lebesgue measure $(V-e)_-\cdot dx$ and the eigenvalues counting
function of the absorption-to-reflection operator on the equipotential surface
$\{V=e\}$.
