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The wavefunction can be rewritten as the exponential of another function {{math|S}} (closely related to the [[Action (physics)|action]]), which could be complex,
<math display="block">\Psi(\mathbf x) = e^{i S(\mathbf{x}) \over \hbar}, </math>
so that its substitution in
<math display="block">i\hbar \nabla^2 S(\mathbf x) - (\nabla S(\mathbf x))^2 = 2m \left( V(\mathbf x) - E \right),</math>
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