Related papers: On 1/Z expansion for two-electron systems
We study a class of exactly solvable models for strongly correlated electrons, defined on a set of N cells, and with infinite on-site repulsion on part of the sites of each cell. For 2N or more electrons the exact ground state is known. We…
We reconsider energy calculations of the spin polarized $\nu=1/2$ Chern-Simons theory. We show that one has to be careful in the definition of the Chern-Simons path integral in order to avoid an IR divergent magnetic ground state energy in…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
It is shown that the non-relativistic ground state energy of helium-like and lithium-like ions with static nuclei can be interpolated in full physics range of nuclear charges $Z$ with accuracy of not less than 6 decimal digits (d.d.) or 7-8…
In this review we first discuss extension of Bohr's 1913 molecular model and show that it corresponds to the large-D limit of a dimensional scaling (D-scaling) analysis, as developed by Herschbach and coworkers. In a separate but synergetic…
The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to $N=9$ electrons for Coulomb as well as for…
We present a general analytic expansion in powers of $1/n$ of the resonant states of quantum-mechanical systems, where $n=1,2,3,\cdots$ is the excitation number. Explicit formulas are obtained for some potential barrier models.
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the…
The energy levels of two interacting electrons in a 2D quantum dot confined by a finite Gaussian potential and subjected to a uniform magnetic field perpendicular to the plane of the dot are studied. Analytic results are obtained for the…
Following detailed analysis of relativistic, QED and mass corrections for helium-like and lithium-like ions with static nuclei for $Z \leq 20$ the domain of applicability of Non-Relativistic QED (NRQED) is localized for ground state energy.…
We consider the pseudorelativistic no-pair Brown-Ravenhall operator for the description of relativistic one-electron ions in a homogeneous magnetic field B. It is shown for central charge not exceeding Z=87 that their ground state energy…
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 generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous…
The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model…
The ground-state wave function and the energy gap are calculated for various layer separations d and for up to 24 electrons by the density matrix renormalization group (DMRG) method. Two-particle distribution function and excitonic…
A systematic nonperturbative scheme is implemented to calculate the ground state energy for a wide class of strongly correlated fermion models. The scheme includes: (a) method of automatic calculations of the cumulants of the model…
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the…
A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two…
The hydrogen negative ion H$^-$ is the simplest two-electron system that exists in nature. This system is not only important in astrophysics but it also serves as an ideal ground to study electron-electron correlations. The peculiar balance…
We show the existence of bound two-electron states in an almost depleted two-dimensional island. These two-electron states are carried by special compact configurations of four single-electron levels. The existence of these states does not…