Related papers: A note about the ground state of the hydrogen mole…
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…
This article continues the series of works by the authors on the approximation of the electronic terms of diatomic molecules by the Morse formula, which is the simplest anharmonic approximation of the real term U(r). Depending on the choice…
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a 1D harmonic potential. At the boundaries both the wave function and its first derivative are continuous and…
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 procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical…
It is shown that the bipolaron ground state is described by a delocalized wave function. For a two-parameter wave function, the lowest variation estimate of the ground state energy in the strong coupling limit is found to be $E=- 0,414125…
The quantum mechanical ground state of a 2D $N$-electron system in a confining potential $V(x)=Kv(x)$ ($K$ is a coupling constant) and a homogeneous magnetic field $B$ is studied in the high density limit $N\to\infty$, $K\to \infty$ with…
The quantum electrodynamic Araki-Sucher correction arising from the interaction between electrons and nuclei is calculated for rovibrational energy levels of the hydrogen molecule and its isotopologues. The corresponding expectation value…
We study by means of exact-diagonalization techniques the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density…
Basics of the Born-Oppenheimer (B-O) approximation are reviewed. Assuming the domain of applicability of B-O approximation is limited to 4 significant digits (s.d.) in energy spectrum, where mass, relativistic and QED corrections do NOT…
The ground-state phase diagram of the asymmetric Hubbard model is studied in one and two dimensions by a well-controlled numerical method. The method allows to calculate directly the probabilities of particular phases in the approximate…
We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the…
We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics nu, 0<= |nu| <= 1, confined in a two-dimensional well (with characteristic frequency omega_0 ) and…
With the recent advances in the development of devices capable of performing quantum computations, a growing interest in finding near-term applications has emerged in many areas of science. In the era of non-fault tolerant quantum devices,…
Hydrogen has been the subject of intense research following the discovery of high-temperature superconductivity in hydrides, and as a result of continuous efforts to produce solid hydrogen. The Born-Oppenheimer approximation is the central…
As quantum computing approaches its first commercial implementations, quantum simulation emerges as a potentially ground-breaking technology for several domains, including Biology and Chemistry. However, taking advantage of quantum…
By using a Coulomb potential modified by the interaction between the magnetic moments of the electron and proton, we have calculated the energy levels of a hydrogen atom. We have obtained fine structure, hyperfine structure and the Lamb…
Asymptotics of the ground state energy of the heavy atoms and molecules in the self-generated magnetic field has been derived and for minimal energy positions of nuclei remainder estimate $O(N^{16/9})$ has been recovered.
In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant $S$ state. It is worth noting that…
This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.