  We consider semi-classical Schr{\"o}dinger operator $ P(h)=-h^2\Delta +V(x)$
in ${\mathbb R}^n$ such that the analytic potential $V$ has a non-degenerate
critical point $x_0=0$ with critical value $E_0$ and we can define resonances
in some fixed neighborhood of $E_0$ when $h>0$ is small enough. If the
eigenvalues of the Hessian are $\zz$-independent the resonances in
$h^\delta$-neighborhood of $E_0$ ($\delta >0$) can be calculated explicitly as
the eigenvalues of the semi-classical Birkhoff normal form. Assuming that
potential is symmetric with respect to reflections about the coordinate axes we
show that the classical Birkhoff normal form determines the Taylor series of
the potential at $x_0.$ As a consequence, the resonances in a
$h^\delta$-neighborhood of $E_0$ determine the first $N$ terms in the Taylor
series of $V$ at $x_0.$ The proof uses the recent inverse spectral results of
V. Guillemin and A. Uribe.
