The ground state (un-normalized) wave function of a given particle is described by:

$\displaystyle \psi_0(x) = e^{\frac{-\alpha^4x^4}{4}}$ with eigenvalue $\displaystyle E_0 = \frac{h^2\alpha^2}{m}$. Determine what the potential is when the particle moves.

The book says the answer is:

V(x)= (1/2m)(h/2pi)^2 alpha^2{(alpha^6)(x^6)-3(alpha^2)(x^2)