In this chapter we introduce the fundamental concepts behind the Green Function Theory. We start from a description of the second quantization method and then, after introducing the ensemble average of an operator, we define the main object of the theory, the Green function. Further on, after obtaining the equation of motion for the Green function, we introduce the self-energy operator and we d...

The most usual asymptotic unconditional method for comparing two independent binomial proportions is the chi-squared test. There are various versions of it (with or without continuity corrections), but there has been no exhaustive study about how they behave, about their optimality, nor about the conditions under which the approximation is considered reliable. In this paper these queries are ex...

Chapter 1. Kinematical electron diffraction 1.1 Electron wavelength 1.2 Plane wave representation of incident electron 1.3 Born approximation and single atom scattering 1.4 Fourier transformation 1.5 Scattering factor and charge density function 1.6 Single scattering theory 1.7 Reciprocal space and reciprocal lattice vector 1.8 Bragg's law and Ewald sphere 1.9 Abbe's imaging theory 1.10 Phase o...

The first absolute se ,3ed measurements, by Lahmam-Bennani et al. [Phys. Rev. A 59, 3548 (1999)], have been recently approximately reproduced by Berakdar [Phys. Rev. Lett. 85, 4036 (2000)] and supported by Jones and Madison [Phys. Rev. Lett. 91, 073201 (2003)], but with widely differing conclusions. The former indirectly implied that the Born-CCC-based calculations of Kheifets et al. [J. Phys. ...

Abstract 3D tomographic phase retrieval under the Born approximation for discrete objects supported on a $n\times n\times n$ grid is analyzed. It proved that $n$ projections are sufficient and necessary unique determination by computed tomography (CT) with full projected field measurements $n+1$ coded diffraction patterns determination, up to global factor, in retrieval. Hence nearly, if not ex...

We show that the so-called "post-Born" effects of weak lensing at 4th order are equivalent to lens-lens couplings in Born Approximation. demonstrate this by explicitly showing equivalence canonical approach using anisotropy remapping method, calculation coupling Boltzmann equation was first developed [Phys. Rev. D89, 123006]. Furthermore, we argue incorporate true effects, i.e. taking into acco...

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of t...

Nowadays it is a standard technique to produce a BoseEinstein condensate in the laboratory [?,?]. In order to build a coherent source of atoms, an atom laser, a major achievement was the coherent extraction of atoms from an atomic trap. At first a pulsed atom laser was built [?,?], recently also continuous wave atom lasers have been realized [?,?]. A short survey over the experimental situation...

A Yukawa-field approximation of the electrostatic free energy of a molecular solvation system with an implicit or continuum solvent is constructed. It is argued through the analysis of model molecular systems with spherically symmetric geometries that such an approximation is rational. The construction extends non-trivially that of the Coulomb-field approximation which serves as a basis of the ...