Related papers: Variational Dirac-Coulomb explicitly correlated co…
We have developed a systematic approach to calculate the correlation function for spin-1/2 particles, incorporating both central and noncentral components of the interparticle interaction. This is achieved by extending the variable phase…
The recently introduced $\kappa$-Poincare-Dirac equation is gauged to treat the $\kappa$-Dirac-Coulomb problem. For the resulting equation, we prove that the perturbation to first order in the quantum group parameter vanishes identically.…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…
Non-covalent interactions are a key ingredient to determine the structure, stability, and dynamics of materials, molecules, and biological complexes. However, accurately capturing these interactions is a complex quantum many-body problem,…
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being…
In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present…
The time dependent Schr\"odinger equation for $\pi^+$--$\pi^-$ pairs, which are emitted from the interaction zone in relativistic nuclear collisions, is solved using wavepacket states. It is shown that the Coulomb enhancement in the…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
We aim to understand how the spectrum of semi-Dirac fermions is renormalized due to long-range Coulomb electron-electron interactions at a topological Lifshitz transition, where two Dirac cones merge. At the transition, the electronic…
The planar quantum dynamics of spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations are obtained directly from the planar Dirac equation with nonminimum coupling. New…
We discuss the Dirac equation in a curved 5-dimensional spherically symmetric space-time. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating space-times with equal angular momenta. It…
Quasi-forbidden electronic transitions in atoms and quasi-degenerate vibronic transitions in molecules serve as powerful probes of hypothetical temporal variations of fundamental constants. Computation of the sensitivity of a transition to…
An accurate non-gradient-expansion based correction to Thomas--Fermi is developed using solvable model. The used model is a system of $N$ non-interacting electrons moving independently in the Coulomb field of the nuclear charge. The…
A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new…
We focus our attention, once again, on the Klein--Gordon and Dirac equations with a plane-wave field. We recall that for the first time a set of solutions of these equations was found by Volkov. The Volkov solutions are widely used in…
The Nikiforov-Uvarov polynomial method employed by Aguda to solve the Dirac equation with an improved Rosen-Morse potential plus a Coulomb-like tensor potential is shown inappropriate because the conditions of its application are not…
The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger equation when a certain potential's type is selected as the Cornell potential. By choosing the generalized…
Contrary to the conventional belief, it was shown that the Breit equation has the eigenvalues for bound states of two oppositely charged Dirac particles interacting through the (static) Coulomb potential. All eigenvalues reduced to those of…