Related papers: Approximate Solutions of Dirac Equation with Hyper…
The Dirac Hamiltonian $H^{\left(D\right)}$ for relativistic charged fermions minimally coupled to (possibly time-dependent) electromagnetic fields is transformed with a purpose-built flow equation method, so that the result of that…
We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave…
We study the dynamics of a two-level crossing model with a parabolic separation of the diabatic energies. The solutions are expressed in terms of the tri-confluent Heun equations --- the generalization of the confluent hypergeometric…
The eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces of arbitrary dimension are computed by separating variables in geodesic polar coordinates. These eigenfunctions are used to derive the heat kernel of the…
It has been observed that a quantum theory need not to be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and we obtain the real relativistic energy eigenvalues and…
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…
A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones…
The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the…
We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schr\"odinger problems defined by the potentials $V(x;\gamma,\eta) = 4\gamma^{2}\cosh^{4}(x) + V_{1}(\gamma,\eta) \cosh^{2}(x) + \eta \left( \eta-1 \right)\tanh^{2}(x)$…
In this study, firstly it is reviewed how the solutions of the Dirac-Weyl equation for a massless charge on the hyperboloid under perpendicular magnetic fields are obtained by using supersymmetric (SUSY) quantum mechanics methods. Then, the…
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive.…
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…
We discuss two different approximation schemes for the self-consistent solution of the {\it relativistic} Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
The Dirac equation with a scalar and an electromagnetic potentials is considered. In the time-harmonic case and when all the involved functions depend only on two spatial variables it reduces to a pair of decoupled bicomplex Vekua-type…
In order to analyse classical electromagnetism in a medium at finite temperature we introduce `an optical density operator', and reformulate Maxwell's equations with the operator, starting from the Dirac-equation-like formulation of…
Based on the results of F. Wilf on the need to take into account the quantum-mechanical correspondence rules in the Dirac equation for an electron, it was shown that the equation obtained by giving physical meaning to $\alpha$-Dirac…