Related papers: Variation and Series Approach to the Thomas-Fermi …
A new procedure of the linear position measurement which allows to obtain sensitivity better than the Standard Quantum Limit and close to the Energetic Quantum Limit is proposed and analyzed in details. Proposed method is based on the…
For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$ we prove a stronger version of Fabry theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
A theory describing above-threshold ionization of atoms and ions in a strong electromagnetic field is presented. It is based on the widely known strong field approximation and incorporates the Coulomb interaction between the photoelectron…
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,…
The particle number projection method is formulated for density dependent forces and in particular for the finite range Gogny force. Detailed formula for the projected energy and its gradient are provided. The problems arising from the…
For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order…
The differential and partially integrated cross sections are considered for bremsstrahlung from high-energy electrons in atomic field with the exact account of this field. The consideration exploits the quasiclassical electron Green's…
We apply the Frobenius method to the Schr\"{o}dinger equation with a truncated Coulomb potential. By means of the tree-term recurrence relation for the expansion coefficients we truncate the series and obtain exact eigenfunctions and…
This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behaviour within lattices at high temperatures in condensed…
Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
Thomas-Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first…
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is…
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate…
Recent theoretical and experimental developments in the field of electron vortex beam physics have raised questions on what exactly this novelty in the field of electron microscopy (and other fields, such as particle physics) really…
Effective potentials of the relativistic m\alpha^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
We propose a novel variational principle in electrostatics and show that one can derive mirror equation in the context of image problem starting from this principle. The corresponding Euler-Lagrange equation is seen to lead to Green's…
The phase behavior of the primitive model of electrolytes is studied in the framework of various mean field approximations obtained recently by means of methods pertaining to statistical field theory (CAILLOL, J.-M., 2004, \textit{J. Stat.…