Related papers: Hydrogen-atom spectrum under a minimal-length hypo…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
There are theoretical frameworks, such as the large extra dimension models, which predict the strengthening of the gravitational field in short distances. Here we obtain new empiric constraints for deviations of standard gravity in the…
We describe bound states, resonances and elastic scattering of light ions using a $\delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients,…
After revival of the concept of minimal length, many investigations have been devoted, in literature, to estimate upper-bound on minimal length for systems like hydrogen atom, deuteron etc. We report here a possible origin of minimal length…
We study the spectral properties of a system of electrons interacting through long-range Coulomb potential on a one-dimensional chain. When the interactions dominate over the electronic bandwidth, the charges arrange in an ordered…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…
Many large scale numerical simulations of astrophysical plasmas must also reproduce the hydrogen ionization and the resulting emission spectrum, in some cases quite accurately. We describe a compact model hydrogen atom that can be readily…
A prolate {\gamma}-rigid regime of the Bohr-Mottelson Hamiltonian within the minimal length formalism, involving an infinite square well like potential in {\beta} collective shape variable, is developed and used to describe the spectra of a…
Coulomb correlations in the optical spectra of semiconductor quantum dots are investigated using a full-diagonalization approach. The resulting multi-exciton spectra are discussed in terms of the symmetry of the involved states.…
An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $\gamma$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in…
As the simplest atom in nature, the hydrogen atom has been explored thoroughly from the perspective of non-relativistic quantum mechanics to relativistic quantum mechanics. Among the research on hydrogen atom, its energy level is the most…
The effect of long-ranged Coulomb interaction on the low energy properties (momentum distribution function, density of states, electron spectral function, and $4k_F$ correlation function) of one-dimensional electron systems is determined…
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…
We calculate the self-energy of one-dimensional electron band with the three-dimensional long range Coulomb interaction within the random phase approximation, paying particular attention to the contribution coming from the electron…
In general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the $\delta'(x)$ potential as a linear kernel of potential energy operator in momentum representation. We find exactly the energy level…
We study the electrical susceptibility of a hydrogen gas at equilibrium, partially ionized by thermal excitations. The gas is described as a quantum plasma of point protons and electrons, interacting via the Coulomb potential. Using the…
For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are…
We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases…
We make a comparison between the energy levels of the hydrogen atom, calculated by using standard methods, and that by using a modified Coulomb potential due to the interaction between the magnetic moments of the proton and electron. In…
The Kratzer's potential $V(r)=g_{1}/r^{2}-g_{2}/r$ is studied in quantum mechanics with a generalized uncertainty principle, which includes a minimal length $\left( \Delta X\right) _{\min}=\hbar\sqrt{5\beta}$. In momentum representation,…