Related papers: Two-dimensional hydrogen-like atom in a weak magne…
In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case…
A charged particle in the presence of a magnetic field is studied in the position dependent operator formalism. Instead of a quantum harmonic oscillator, the solution of the resulting Schr\"odinger-like equation is the one for the Morse…
A variational treatment for a two-electron quantum dot (the artificial helium atom) is proposed which leads to exact answer for the ground state energy. Depending on the magnetic field value the singlet-triplet and triplet-triplet…
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…
In the present work we study the effect of unparticle modified static potentials on the energy levels of the hydrogen atom. By using Rayleigh-Schr\"odinger perturbation theory, we obtain the energy shift of the ground state and we compare…
By an extension of the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistical properties of a hydrogen atom in a uniform magnetic field. In the…
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…
Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the…
The first in m/M and fourth in Z\alpha (pure recoil) correction to a hydrogen energy level is found. This correction comprises two contributions, one coming from the atomic scale, the other from distances of the Compton wavelength order.…
The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a…
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, with the self-generated magnetic field, and, in particular, to derive relativistic Scott…
We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order…
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method, we calculate the energy eigenvalues of the 1S, 2P- and 3D- levels. We compare the computed…
We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the potential part of the Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb one and…
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a genera lization of virial theorem, which consists in scaling the wave function, we…
In this manuscript we provide a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms.
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…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…
In this paper, we use Clifford algebra $Cl_{2,0}$ to find the 2D orbit of Hydrogen electron under a Coulomb force and a perturbing circularly polarized electric field of light at angular frequency~$\omega$, which is turned on at time $t =…