Any known way to diagonalize the Hamiltonian of a charge particle in a EM field?

Consider the Hamiltonian of a free (charged) particle, i.e.,
$$
H = frac{p^2}{2m}.
$$
This is easily "diagonalized" by wave functions $e^{ikx}$ (where I’m speaking loosely of diagonalization since $e^{ikx}$ are not eigenstates in the Hilbert space $L^2$. Of course, we could regularize the problem by considering the Hamiltonian on a finite lattice with periodic boundary condition so that wave functions are indeed eigenstate.)

If we were to add a EM field, then by minimal coupling, the Hamiltonian becomes
$$
H = frac{1}{2m}(p-eA)^2 +evarphi
$$
Question. Is there an analytic or operator-based solution (e.g., latter operators) of diagonalizing this minimally-coupled Hamiltonian (we can ignore $varphi$ if that helps)? If this problem is not regularized, we could also think of Peierls substitution of a second-quantized hopping Hamiltonian on a finite lattice with periodic boundary conditions, i..e,
$$
H= sum_{i,j} t_{ij} c_i^* exp{(-iA_{ij})} c_j
$$