Related papers: Non-local PT-symmetric potentials in the one-dimen…
Finite size effects alter not only the energy levels of small systems, but can also lead to new effective interactions within these systems. Here the problem of low energy quantum scattering by a spherically symmetric short range potential…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain the two-point Green's function of the relativistic Dirac-Morse problem. This is accomplished by setting up the…
The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show…
We consider $1+1$-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Poschl-Teller potentials and obtain their solution in terms of…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
We study $(2+1)$ dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another…
We compare two different solutions of the Dirac equation in (1+1) dimensions. One solution is for a fermion in the presence of an electric potential and the other is for a fermion in the presence of a pseudoscalar potential. It is shown…
We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for…
Several kernel-based methods for the numerical solution of fractional differential equations have been developed in the recent past; however, these techniques exclusively relied on the use of radial basis function approximations. In the…
Spin-polarized symmetric nuclear matter is studied within the Dirac-Brueckner-Hartree-Fock approach. We pay particular attention to the difference between the one-body potentials of upward and downward polarized nucleons. This is formally…
We study the self-interaction effects for the Dirac particle moving in an external field created by static charges in (1+1)-dimensions. Assuming that the total electric charge of the system vanishes, we show that the asymptotically linearly…
The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…
The goal of this paper is to provide an intuitive and useful tool for analyzing the impurity bound state problem. We develop a semiclassical approach and apply it to an impurity in two dimensional systems with parabolic or Dirac like bands.…
We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional P\"oschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the…
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scaterring and the Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a…
Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these…
The one dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the…
We study the Darboux transformation (DT) for Dirac equations with (1+1) potentials. Exact solutions for the adiabatic external field are constructed. The connection between the exactly soluble Dirac (1+1) potentials and the soliton…