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Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
The relation
$$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$
satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$.
Now let's think in the reverse direction.
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