Related papers: Exact Green's function for rectangular potentials …
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…
Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the…
In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an…
For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is,…
We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the square and the edges and corners of the cube. The main idea…
Exact Green's functions related to Dirac particle submitted to the combination of Aharonov-Bohm and Coulomb fields in (2+1) coordinate space are analytically calculated via path integral formalism in both global and local representations.…
We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an…
In this paper we obtain the explicit expression of the Green's function related to a general $n$ order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, a $n$ dimensional parameter…
We discuss recent \emph{ab initio} calculations based on self-consistent Green's function theory. It is found that a simple extension of the formalism to account for two-nucleon scattering outside the model space allows to calculate…
The single-particle nuclear potential is intrinsically nonlocal. In this paper, we consider nonlocalities which arise from the many-body and fermionic nature of the nucleus. We investigate the effects of nonlocality in the nuclear potential…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or…
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrodinger equation in two dimensional space. The system considered in this work is a quantum particle that have an…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
An improved form of the Tietz potential for diatomic molecules is \ discussed in detail within the path integral formalism. The radial Green's function is rigorously constructed in a closed form for different shapes of this potential. For…
We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit…
In formal scattering theory, Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm-Liouville theory to compute Green functions within a rigorous mathematical theory. We shall show that both…