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\end{equation}  Try an example. If we take a moving ball of mass $m$, and velocity $v$ and wait for it to move from $A$ to $B$ seperated by a distance $d$, the kinetic energy $\epsilon=\frac{1}{2}mv^2$ and therefore the time taken to get from $A$ to $B$ is \begin{equation}  t(\epsilon)=\sqrt{\frac{m}{2E}}d  \end{equation}  Performing the integral to set up the iterative scheme would give \begin{equation}  E_i=\frac{1}{\tau}\int_0^{E_{i-1}} \sqrt{\frac{m}{2E}}d \; \mathrm{d\epsilon}=\frac{d}{2\tau}\sqrt{\frac{m}{2}}E_{i-1}^1/2  \end{equation}  Now take a quantum system with a Hamiltonian $\hat{H}$, and wavefunctions $\Psi_i$ we know that \begin{equation}  \hat{H}\Psi_i=E_i\Psi_i \\