Related papers: Experiment and Theory in Computations of the He At…
Recently reported computations have been extended to give ten more decimals of accuracy in the ground state energy of the Schrodinger equation for the idealized Helium atom. With the F basis - Hylleraas coordinates with negative powers and…
The leading relativistic and QED corrections to the ground state energy of the three-body system (epe) are calculated numerically using a Hylleraas correlated basis set. The accuracy of the nonrelativistic variational ground state wave…
A simple expression for a ground state energy for a two-electron atom is derived. For this, assumption based upon the Niels Bohr ''old'' quantum mechanics idea about electron correlation in a two-electron atom is exploited. Results are…
The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy…
We discuss an approach to accurate numerical computations of slowly convergent properties in two-electron atoms/ions which include the negatively charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively charged,…
We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and Be$^+$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis…
The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that…
Highly accurate nonrelativistic ground-state wave function and energy of the lithium atom is obtained in the Hylleraas basis set. The leading relativistic corrections,as represented by Breit-Pauli Hamiltonian, are obtained in fair agreement…
Several ultra-compact accurate wave functions in the form of generalized Hylleraas-Kinoshita functions and Guevara-Harris-Turbiner functions, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC), or,…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…
Some typical overlap/potential energy integrals which occur in the use of extended Hylleraas-configuration interaction (E-Hy-CI) functions with Slater-type orbital (STO) basis for two-electron atomic structure calculations, have been…
A trial function is presented for the $H_2$ molecule which provides the most accurate (the lowest) Bohr-Oppenheimer ground state energy among few-parametric trial functions (with $\leq 14$ parameters). It includes the electronic correlation…
Bohr's model agreed with the hydrogen spectrum results, but did not agree with the spectrum of Helium. Here we show that Bohr's model-based methods can calculate the experimental value (-79.005 eV) of Helium ground state energy correctly.…
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
The total energies and various bound state properties of the excited $2^1S(L = 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He, ${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy. The…
We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a…
Variational, nonrelativisitic energies have been calculated for the ground state ($^3P_g$) and the lowest quintuplet state ($^5S_u$) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated…
Considering the nuclear motion, the authors give out the nonrelativistic ground energy of a helium atom by using a simple but effective variational wave function with a flexible parameter $k$. Based on this result, the relativistic and…
The problem of calculating the four--nucleon bound state properties for the case of realistic two- and three-body nuclear potentials is studied using the hyperspherical harmonic (HH) approach. A careful analysis of the convergence of…