Related papers: The Energy Eigenvalues of the Two Dimensional Hydr…
We calculate the atomic structure of hydrogen and helium, atoms and molecules in an intense magnetic field, analytically and numerically with a judiciously chosen basis.
Energy levels of hydrogen are calculated as one-loop matrix elements of the QED energy-momentum tensor trace in the external field approximation. An explicit connection established between the one-loop trace diagrams and the standard Lamb…
In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schr\"odinger equation in…
We present a study of the spectral properties like the energy spectrum, the eigenmodes and density of states of a classical finite system of two-dimensional (2D) charged particles which are confined by a quadratic potential. Using the…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and…
The first order perturbations of the energy levels of a stationary hydrogen atom in static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P,…
We calculate the single-particle states of a two-dimensional electron gas (2DEG) in a perpendicular quantizing magnetic field, which is periodic in one direction of the electron layer. We discuss the modulation of the electron density in…
In this work, we study how the combination of rotation and a topological defect can influence the energy spectrum of a two dimensional electron gas in a strong perpendicular magnetic field. A deviation from the linear behavior of the energy…
The non-relativistic energy levels of ortho-positronium are calculated in the quadrupole and octupole approximations for the interaction potential. For this purpose, the RST eigenvalue problem of angular momentum is illustratively solved…
The electronic energy of $\mathrm H_2^+$ in magnetic fields of up to $B=0.2B_0$ (or 4.7 $\times 10^4$ Tesla) is investigated. Numerical values of the magnetic susceptibility for both the diamagnetic and paramagnetic contributions are…
The resonant spectra of hydrogen and anti-hydrogen atoms in the presence of an external electric field are compared theoretically. It is shown that nonresonant corrections to the transition frequency contain terms linear in the electric…
Energies and spatial observables for the $^1\Sigma_g$ state of the hydrogen molecule in magnetic fields parallel to the proton-proton axis are calculated with a guided random walk Feynman-Kac algorithm. We demonstrate that the accuracy of…
A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state ${}^3\Pi_u$ of the hydrogen molecule ${\rm H}_2$ in strong magnetic field ${\bf B}$ in…
We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$H=((D-A)\cdot\boldsymbol{\sigma})^2-V$$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a…
We study the thermodynamic properties of a partially ionized hydrogen plasma in strong magnetic fields, B ~ 10^{12}-10^{13} G, typical of neutron stars. The properties of the plasma depend significantly on the quantum-mechanical sizes and…
We study a method to induce resonant transitions between antihydrogen quantum states above a material surface in the gravitational field of the Earth. The method consists in applying a gradient of magnetic field which is temporally…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
We study orbital magnetism of a degenerate electron gas in a number of two-dimensional integrable systems, within linear response theory. There are three relevant energy scales: typical level spacing, the energy related to the inverse time…
The electron states in a size-quantaized coated semiconductor wire in a uniform magnetic field applied parallel to the wire axis is considered. The wave functions are found and the equation for determination of energy eigenvalues depending…