  For a large class of quantum mechanical models of matter and radiation we
develop an analytic perturbation theory for non-degenerate ground states. This
theory is applicable, for example, to models of matter with static nuclei and
non-relativistic electrons that are coupled to the UV-cutoff quantized
radiation field in the dipole approximation. If the lowest point of the energy
spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this
eigenvalue is an analytic function of the nuclear coordinates and of
$\alpha^{3/2}$, $\alpha$ being the fine structure constant. A suitably chosen
ground state vector depends analytically on $\alpha^{3/2}$ and it is twice
continuously differentiable with respect to the nuclear coordinates.
