  In this article is proved the existence and uniqueness of a minimizer of the
energy for the non-relativistic one electron Pauli-Fierz model, within the
class of pure quasifree states. The minimum of the energy on pure quasifree
states coincides with the minimum of the energy on quasifree states. Infrared
and ultraviolet cutoffs are assumed, along with sufficiently small coupling
constant and momentum of the dressed electron. A perturbative expression of the
minimum of the energy on quasifree states for a small momentum of the dressed
electron and small coupling constant is then given. We also express the
Lagrange equation for the minimizer, in terms of the generalized one particle
density matrix of the pure quasifree state.
