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We consider systems of static nuclei and electrons {atoms and molecules{ coupled to the quantized radiation eld. The interactions between electrons and the soft modes of the quantized electromagnetic eld are described by minimal coupling, ~ p! ~ p e ~ A(~x), where ~ A(~x) is the electromagnetic vector potential with an ultraviolet cuto . If the interactions(More)
A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map. It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel(More)
We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely lled or completely empty. The only assumption needed is that the two-body interaction is| like the Coulomb interaction|repulsive; it could, however, be more complicated than a simple potential, e.g., it could have tensor(More)
We consider a system of nitely many non-relativistic electrons bound in an atom or molecule which are coupled to the electromagnetic eld via minimal coupling or the dipole approximation. Among a variety of results, we give suucient conditions for the existence of a ground state (an eigenvalue at the bottom of the spectrum) and resonances (eigenvalues of a(More)
This work addresses the problem of infrared mass renormalization for a scalar electron in a translation-invariant model of non-relativistic QED. We assume that the interaction of the electron with the quantized electromagnetic field comprises a fixed ultraviolet regularization and an infrared regularization parametrized by σ > 0. For the value p = 0 of the(More)
We estimate the accuracy of the mean eld approximation induced by the Thomas-Fermi potential for the ground state energy of atoms and molecules. Taking the Dirac exchange correction into account, we show the error to be of the form O(Z 5=3?) + D for any < 2=231 as the total nuclear charge Z becomes large. D is an electrostatic energy of the diierence(More)