Related papers: Dirac Equation in Noncommutative Space for Hydroge…
This paper calculates the quantized energy levels of the hydrogen atom, using a metaplectic-c prequantization bundle and a definition of a quantized energy level that was introduced by the author in a previous paper. The calculation makes…
The spectrum of the Dirac oscillator perturbed by the Coulomb potential is considered. The Regge trajectories for its bound states are obtained with the method of $\hbar$-expansion. It is shown that the split of the degenerate energy levels…
Based on the precision experimental data of energy-level differences in hydrogenlike atoms, especially the 1S-2S transition of hydrogen and deuterium, the necessity of establishing a reduced Dirac equation (RDE) with reduced mass as the…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
We re-examine the non Hermitian position coordinate of Dirac's equation, in the light of his own insights and conclude that this, and the Dirac equation itself is symptomatic of an underlying Noncommutative Geometry.
Motivated by the long-debated question about the internal stability of the electron, the force densities acting on the charge density of the 1s electron in the H atom are investigated. The problem is mapped onto the canonical formalism for…
The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i, P_j] = i\hbar\{\delta_{ij}(1+\beta P^2) + \beta'P_iP_j\}$ is determined both numerically and perturbatively for arbitrary values of $\beta'/\beta$…
In order to investigate whether space coordinates are intrinsically noncommutative, we make use of the Hall effect on the two-dimensional plane. We calculate the Hall conductivity in such a way that the noncommutative U(1) gauge invariance…
In this article, we define two-particle system in Coulomb potential for twist-deformed space-time with spatial directions commuting to time-dependent function $f_{\kappa_a}({t})$. Particularly, we provide the proper Hamiltonian function and…
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…
We study the Dirac and the klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a…
Precise solutions of the Hartree-Fock equations for the ground state of the hydrogen molecule are obtained for a wide range of internuclear distances R by means of a two-dimensional fully numerical mesh computational method. The spatial…
We show that a free Dirac quantum field on a globally hyperbolic spacetime has the following structural properties: (a) any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent; (b) the…
We investigate the effects of long range Coulomb interactions on the low-temperature properties of a second-order Dirac semimetal in terms of the renormalization group. In contrast to the first-order Dirac semimetal, the full rotation…
We propose a manifestly Lorentz covariant, non-commutative Dirac equation for charged particles interacting with an electromagnetic field. The equation is formulated on the operator level, but operators are not composed through the normal…
The system describing a single Dirac electron field coupled with classically moving point nuclei is presented and studied. The model is a semi-relativistic extension of corresponding time-dependent one-body Hartree-Fock equation coupled…
We study a classical model of Helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as…
The linear Stark effect in the MIC-Kepler problem describing the interaction of charged particle with Dirac's dyon is considered. It is shown that constant homogeneous electric field completely removes the degeneracy of the energy levels on…
Using elements of symmetry, as gauge invariance, several aspects of a Schr\"odinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a…
The noncommutativity of a four-dimensional phase space is introduced from a purely symplectic point of view. We show that there is always a coordinate map to locally eliminate the gauge fluctuations inducing the deformation of the…