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We solve the Dirac equation approximately for the attractive scalar $S(r)$ and repulsive vector $V(r)$ Hulth\'{e}n potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number $\kappa .$ In the…
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
The exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders are used for deriving the exact expressions of the relativistic partial currents. It is shown that these…
In this paper, we determine the bound-state solutions for Dirac fermions with electric dipole moment (EDM) and position-dependent mass (PDM) in the presence of a radial magnetic field generated by magnetic monopoles. To achieve this, we…
We present a relativistic analysis of fermions in an external electric field by non-perturbatively solving the Dirac equation with a static gauge. Different from the magnetic field effect, the fermion wave function in an electric field…
The relativistic theory of the Dirac fermions moving on cylinders in external Aharonov-Bohm field is built starting with a suitably restricted Dirac equation whose spin degrees of freedom are not affected. The exact solutions of this…
We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy…
A special class of Dirac-Pauli equations with time-like vector potentials of external field is investigated. A new exactly solvable relativistic model describing anomalous interaction of a neutral Dirac fermion with a cylindrically…
In this work, we investigate the quantum motions of non-relativistic particles interacting with a potential in the presence of the Aharonov-Bohm (AB) flux field within a topological defect geometry, for example, space-time with a distortion…
The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding…
We investigate the relativistic effects of a moving particle in the field of a pseudo-harmonic oscillatory ring-shaped potential under the spin and pseudo-spin symmetric Dirac wave equation. We obtain the bound state energy eigenvalue…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be…
The creation of charged fermions from the vacuum by a Coulomb field in the presence of an Aharonov--Bohm (AB) potential are studied in 2+1 dimensions. The process is governed by a (singular) Dirac Hamiltonian that requires the supplementary…
We investigate on the plane the axial anomaly for euclidean Dirac fermions in the presence of a background Aharonov--Bohm gauge potential. The non perturbative analysis depends on the self--adjoint extensions of the Dirac operator and the…
The behaviour of fermions in the background of a double-step potential is analyzed with a general mixing of scalar and vector couplings via continuous chiral-conjugation transformation. Provided the vector coupling does not exceed the…
We have generalized the solutions of the radial Dirac equation with a tensor potential under spin and pseudospin symmetry limits to exceptional orthogonal Hermite polynomials family. We have obtained new general rational potential models…
We constrain the possible bound-state solutions of the spinless Salpeter equation (the most obvious semirelativistic generalization of the nonrelativistic Schr\"odinger equation) with an interaction between the bound-state constituents…
We discuss the construction and properties of rigidly-rotating states for free scalar and fermion fields in quantum field theory. On unbounded Minkowski space-time, we explain why such states do not exist for scalars. For the Dirac field,…