Related papers: Exact solutions to the Dirac equation for a Coulom…
We prove that for the radial Dirac equation with Coulomb-type potential the generalized dynamical scattering operator coincides with the corresponding generalized stationary scattering operator. This fact is a quantum mechanical analogue of…
The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum $L$. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and…
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown…
It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
The Dirac equation is considered in the background of potentials of several types, namely scalar and vector-potentials as well as "Dirac-oscillator" potential or some of its generalisations. We investigate the radial Dirac equation within a…
The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us…
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…
Covergent eigensolutions of the Dirac Equation for a relativistic electron in an external Coulomb potential are obtained using the Lanczos Algorithm. A tri-diagonal matrix representation of the Dirac Hamiltonian operator is constructed…
We propose a symmetry of the Dirac equation under the interchange of signs of eigenvalues of the Dirac's $K$ operator. We show that the only potential which obeys this requirement is the Coulomb one for both vector and scalar cases.…
Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
This article illustrates the bound states of Kemmer equation for spin-1 particles. The asymptotic, exact and Coulomb field solutions are obtained by using action principle. In the conclusion the energy spectrum of spin-1 particles moving in…
In this work the Dirac oscillator in $(2+1)$ dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter $s$ and angular momentum quantum number $m$. Contrary…
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…
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…
We decouple the Dirac's radial equations in $D+1$ dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an…
New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the…