If $-i \frac{ \partial}{\partial x}$ becomes $p$ in the momentum basis, I would expect the energy to be the same:
$$i\frac{\partial}{\partial t} \to E$$
So the time dependent Schrödinger equation becomes:
$$E\psi=H\psi$$
But I believe the $E$ is variable unlike the time independent one which is constant. Is this the case?
