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k^4/k^2 +k^2  \end{equation}  Start Here:  We are seeking a functional transformation, a functional on $V(x)$ such that for any given $V(x)$ we can predict the wavefunction of a system. That is, the direct relationship \begin{equation}  \psi(x)=F(V(x))  \end{equation}  We use the folding transforms as candidate functions for $F()$.