Hamiltonian in momentum representation

What I understand about momentum representation is quite elementary: you replace $\frac{\hbar}{i}\frac{\partial}{\partial x}$ with $p$ and $x$ with $i\hbar\frac{\partial}{\partial p}$.

In this document the author starts from the following Hamiltonian

$ H = \int dr \psi^+(r) [-\frac{\hbar^2 \nabla^2}{2m} +\sum_i V(r-r_i)] \psi(r)$

Where $\psi^+$ and $\psi$ are creation and annihilation field operators and the potential contains actually disorder in the form of the position of scatterers.

Then the author says that in momentum representation the Hamiltonian is

$ H = \sum_k \epsilon_k n_k + \sum_i \sum_k V_k exp(ik.r_i) \rho_k$

where we has the dispersion relation $\epsilon_k = \frac{\hbar^2 k^2}{2m}$

How did this derivation happen? Is there some Fourier transform that took place?