Vrftjkry

Let us assume we consider a problem of free electrons in an external
electric field
$$hat{H}(mathbf{r})=-frac{hbar^2}{2m}nabla^2-ePhi(mathbf{r},t),$$
where $-nabla Phi(mathbf{r},t) =Emathbf{e}_x$.
Show that the Hamilton operator can be written into the form
$$hat{H}(mathbf{r},mathbf{R}(t))=frac{1}{2m}left(-ihbar nabla+mathbf{R}(t)right)^2,$$
where $mathbf{R}(t) = emathbf{A}'(t)$. Here, $mathbf{A}'(t)$ is the vector potential after we have exploited the gauge freedom of the electromagnetic potentials
$$mathbf{E}(mathbf{r},t)=Emathbf{e}_x=-nabla Phi'(mathbf{r},t)-frac{partial}{partial t}mathbf{A}'(t).$$

I know that the electromagnetic potential have the property of gauge invariance given by
$$mathbf{A}' to mathbf{A} +nabla chi$$
$$Phi' to Phi -frac{partial chi}{partial t}$$
where we took $c=1$ for simplicity. Looking at the Hamiltonian, it suggests that $mathbf{A}(t)=0$, so that $mathbf{A}'=nabla chi$.

I've tried to plug in the parameter $mathbf{R}(t)$ into the Hamiltonian I should write (the one dependant on $mathbf{R}(t)$), but I don't get the first one.

Any suggestions? Any help would be appreciate.