A particle of mass m is in the state:\(Ψ(x,t) = A e^{-\alpha \left(\frac{mx^2}{\hbar} + it\right)}\)
where A and α are positive real constants. For what potential energy function V(x) does Ψ satisfy the Schrödinger equation?
1
\(V(x) = max^3\)
2
\(V(x) = 2max^3\)
3
\(V(x) = 2ma^2x^2\)
4
\(V(x) = ma^2x^2\)