Exact ground state of a solvable sextic potential
= Exact ground state of a solvable sextic potential
For
$$
V(x)=\frac{\hbar^2}{2m}(x^6-3x^2+2),
$$
the nodeless wavefunction $e^{-x^4/4}$ is an exact eigenstate with energy $\hbar^2/m$, and hence is the ground state.