Related papers: Majorana solutions to the two-electron problem
After a quick historical account of the introduction of the group-theoretical description of Quantum Mechanics in terms of symmetries, as proposed by Weyl, we examine some unpublished papers by Ettore Majorana. Remarkable results achieved…
Fully relativistic approach to evaluate the correlation effects in highly charged ions is presented. The interelectronic-interaction contributions of first and second orders in $1/Z$ are treated rigorously within the framework of…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a…
Electron-electron correlation forms the basis of difficulties encountered in many-body physics. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in the correlation. In an…
The quantum electrodynamics formalism to treat the interelectronic-interaction correction of first order in $1/Z$ to the two-electron part of the nuclear recoil effect on binding energies in atoms and ions is developed. The nonperturbative…
We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced…
It is demonstrated, how the theoretical analysis preceding the numerical calculations helps to calculate the energy of the ground state of helium atom, and enables to avoid qualitative errors in the calculations of the characteristics of…
A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\alpha$ is presented for the ground and $n = 2$ excited states of helium-like ions. After subtracting the first terms of the $Z\alpha$…
The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon…
Neutrinoless double-beta decay is a hypothesized process where in some even-even nuclei it might be possible for two neutrons to simultaneously decay into two protons and two electrons without emitting neutrinos. This is possible only if…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This…
The $1/Z$-expansion for the Coulomb system of infinitely massive center of charge Z and two electrons is discussed. Numerical deficiency in Baker et al, {\em Phys. Rev. \bf A41}, 1247 (1990) is indicated which continue to raise doubts in…
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…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
We discuss a method of solving the time dependent Schrodinger equation for atoms with two active electrons in a strong laser field, which we used in a previous paper [A. Scrinzi and B. Piraux, Phys. Rev. A 56, R13 (1997)] to calculate…
An account is given of an interesting but unknown theory by Majorana regarding scalar quantum electrodynamics, elaborated several years before the known Pauli-Weisskopf theory. Theoretical calculations and their interpretation are given in…
The electron self-energy (self-mass) is calculated on the basis of the model of quantum field theory with maximal mass M, developed by V.G.Kadyshevsky et al. within the pseudo-Hermitian quantum electrodynamics in the second order of the…