相关论文: Positivity and lower bounds to the decay of the at…

We study electron densities of eigenfunctions of atomic Schroedinger operators. We prove the existence of rho~'''(0), the third derivative of the spherically averaged atomic density rho~ at the nucleus. For eigenfunctions with corresponding…

Lower bound for ${\bar \rho}''(0)$, the second derivative of the spherically averaged atomic electronic density at the nucleus, and upper bound for ${\bar \rho}'''(0)$, the third derivative, are obtained respectively. It is shown that, for…

With a special `Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, $\sup_{y\in B(x,R)}|\nabla\psi(y)| \leq C(R) \sup_{y\in B(x,2R)}|\psi(y)|$…

We consider a pseudorelativistic model of atoms and molecules, where the kinetic energy of the electrons is given by $\sqrt{p^2+m^2}-m$. In this model the eigenfunctions are generally not even bounded, however, we prove that the…

A new formula that relates the electron density at the nucleus of atoms,rho(0,Z), and the atomic number,Z, is proposed. This formula,rho(0,Z)=a(Z-bZ^(0.5))^3, contains two unknown parameters (a,b) that are derived using a least square…

The average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0,L] is derived. Our method relies on the eigenvalues distributions (extreme value statistics problem) which are…

Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster…

We prove that the electronic density of atomic and molecular eigenfunctions is smooth away from the nuclei. The result is proved without decay assumptions on the eigenfunctions.

We derive an upper estimate for electronic density $\rho_\Psi (x)$ in heavy atoms and molecules. While not sharp, on the distances $\gtrsim Z^{-1}$ from the nuclei it is still better than the known estimate $CZ^3$ ($Z$ is the total charge…

We investigate regularity properties of molecular one-electron densities rho near the nuclei. In particular we derive a representation rho(x)=mu(x)*(e^F(x)) with an explicit function F, only depending on the nuclear charges and the…

It is known that the asymptotic decay of the electron density $n(\br)$ outside a molecule is informative about its first ionization potential $I_0$, $n(|\br|\to\infty) \sim \text{exp}(-2\sqrt{2I_0}\,r)$. This dictates the orbital energy of…

The equations determining the energy density $\rho$ of a gas of photons in thermodynamic equilibrium with a spherical mass $M$ at a non-zero temperature $T_s>0$ is derived from Einstein's equations. It is found that for large $r$, $\rho…

The rho-meson mass shift, width broadening, and spectral density at finite temperature and nucleon density are estimated using a general formula which relates the self-energy to the real and imaginary parts of the forward scattering…

We analyze through the expectation value of the energy density the spatial nonlocality of single photons emitted by the spontaneous decay of a Hydrogen atom. By using a minimal coupling between the quantized electromagnetic field and the…

We present a unified model describing electroweak properties of the pi and rho mesons. Using a general method of relativistic parametrization of matrix elements of local operators, adjusted for the nondiagonal in total angular momentum…

Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using the Pekeris-like method, the ground state wave functions $\Psi$ of the helium-like atoms with nucleus charge $1\leq…

Consider a bound state (an eigenfunction) $\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\gamma$ and of the one-particle kinetic energy density matrix $\tau$ associated with $\psi$. The paper…

A basic quantity in the characterization of relativistic particles is the proton-to-electron (p/e) energy density ratio. We derive a simple approximate expression suitable to estimate this quantity, U_p/U_e = (m_p/m_e)^(3-q)/2, valid when a…

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.

As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this work we explore the extension…