相关论文: Proof of the Strong Scott Conjecture for Chandrase…
We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic energy $(c^2p^2+c^4)^{1/2}-c^2$ used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the…
The strong Scott conjecture about the electron density at a distance 1/Z from an atomic nucleus of charge $Z$ and its generalization for molecules are proved. The density, suitably scaled, converges to an explicit limiting density as $Z \to…
We consider a large neutral atom of atomic number $Z$, modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas--Fermi length scale $Z^{-1/3}$. Using an…
In heavy atoms and molecules, on the distances $a \ll Z^{-1/3}$ from one of the nuclei (with a charge $Z_m$) we prove that $\rho_\Psi (x)$ is approximated in $L^p$-norm, by the electronic density for a single atom in the model with no…
We prove the convergence of the density on the scale $Z^{-1}$ to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known to describe heavy atoms accurately.
We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction, exists. It turns out to be lower than in the…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
In this paper we study the large-Z behaviour of the ground state energy of atoms with electrons having relativistic kinetic energy sqrt(p^2c^2+m^2c^4)-mc^2. We prove that to leading order in Z the energy is the same as in the…
The neutron spin-orbit density contributes to the nuclear charge density as a relativistic effect. The contribution is enhanced by the effective mass stemming from the Lorentz-scalar potential in relativistic models. This enhancement…
Motivated by the long-debated question about the internal stability of the electron, the force densities acting on the charge density of the 1s electron in the H atom are investigated. The problem is mapped onto the canonical formalism for…
We prove an optimal upper bound for the density of electrons of an infinite Bohr atom (no electron-electron interactions) described by the relativistic operators of Chandrasekhar and Dirac. We also consider densities in each angular…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, with the self-generated magnetic field, and, in particular, to derive relativistic Scott…
We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation…
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schr\"odinger perturbation theory, with the use of the Sturmian series expansion of the generalized…
Imposing the Born rule as a fundamental principle of quantum mechanics would require the existence of normalizable wave functions also for relativistic particles. Indeed, the Fourier transforms of normalized k-space amplitudes yield…
The cosmic censorship hypothesis, introduced by Penrose forty years ago, is one of the corner stones of general relativity. This conjecture asserts that spacetime singularities that arise in gravitational collapse are always hidden inside…
A unified approach to the calculation of dispersive forces on ground-state bodies and atoms is given. It is based on the ground-state Lorentz force density acting on the charge and current densities attributed to the polarization and…
Static spherically symmetric solution of the Einstein's equations is found representing averaged properties of an infinite self-gravitating gas in the dynamical equilibrium. It depends upon three parameters: the core radius, the…