  We revisit the problem posed by an anharmonic oscillator with a potential
given by a polynomial function of the coordinate of degree six that depends on
a parameter $\lambda $. The ground state can be obtained exactly and its energy
$E_{0}=1$ is independent of $\lambda $. This solution is valid only for
$\lambda >0$ because the eigenfunction is not square integrable otherwise. Here
we show that the perturbation series for the expectation values are Pad\'{e}
and Borel-Pad\'{e} summable for $\lambda >0$. When $% \lambda <0$ the spectrum
exhibits an infinite number of avoided crossings at each of which the
eigenfunctions undergo dramatic changes in their spatial distribution that we
analyze by means of the expectation values $\langle x^{2}\rangle $.
