Related papers: Julian Schwinger and the Semiclassical Atom
The chemical potiential for the ground states of the atomic elements have been calculated within the semiclassical approximation The present work closely follows Schwinger and Englert's semiclassical treatment of atomic structure.
The semi-classical approach leading to the Thomas-Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of…
We investigate a semiclassical momentum density energy functional for atoms and show that it yields the same value as the well-known Thomas-Fermi functional. In fact, we show an explicit relation between the minimizers of the two…
Julian Schwinger (1918--1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as…
Julian Schwinger became interested in the Casimir effect in 1975. His original impetus was to understand the quantum force between parallel plates without the concept of zero point fluctuations of field quanta, in the language of source…
We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy,…
Julian Schwinger's influence on twentieth century science is profound and pervasive. Of course, he is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize with Richard Feynman and…
We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage that the full quantized model is solvable and equivalent to a (massive) gauge field…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is…
Julian Schwinger's influence on Twentieth Century science is profound and pervasive. Of course, he is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize with Richard Feynman and…
A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schr\"odinger equation and a discussion of semiclassical time as well…
Properties of the fractional Schrodinger equation have been studied. We have proven the hermiticity of fractional Hamilton operator and established the parity conservation law for the fractional quantum mechanics. As physical applications…
The energy spectra of atomic ions are re-examined from the point of view of Thomas-Fermi scaling relations. For the first ionization potential, which sets the energy scale for the true discrete spectrum, Thomas-Fermi theory predicts the…
In this paper we study the semiclassical limit of the Schr\"odinger equation. Under mild regularity assumptions on the potential $U$ which include Born-Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic…
The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory.…
We consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators $H_Z^{\text{TF}}=-\Delta-\Phi_Z^{\text{TF}}$ in three-dimensional space, where $Z$ is the nuclear charge of the atom and…
In 1953 Casimir proposed a semiclassical model for the electron based on the concept that net inward radiation pressure from the electromagnetic vacuum fluctuations fields (as in the Casimir effect, generally) might play the role of…
The physical model of a nonrelativistic quantized Schrodinger's electron (SE) is offered. The behaviour of the SE well spread elementary electric charge had been understood by means of two independent and different in a frequency and size…