Related papers: Quaternionic Dirac free particle
Starting with the quaternionic Minkowski space-time and its four-vector representation, a rotational analogue of the quaternionic Dirac equation in the electromagnetic field is developed, which includes not only the energy solutions but…
We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or…
In the model of topological particles we have four types of topologically stable dual Dirac monopoles with soft core and finite mass. We discuss the steps how to get a Dirac equation for these particles. We show for the free and the…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…
It has been observed that a quantum mechanical theory need not to be Hermitian to have a real spectrum. In this paper we obtain the eigenvalues of a Dirac charged particle in a complex static and spherically symmetric potential.…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and…
It is shown that the hypercomplex Dirac equation describes the system of connected fields: 4-scalar, 4-pseudoscalar, 4-vector, 4-pseudo-vector and antisymmetric 4-tensor second rank field. If mass is assumed to be zero this system splits…
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 idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffman's work on discrete physics, iterants and Majorana Fermions and the work…
The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, has been cast in terms of a new set of…
On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier…
By employing a pseudo-orthonormal coordinate-free approach, the Dirac equation for particles in the Kerr--Newman spacetime is separated into its radial and angular parts. In the massless case to which a special attention is given, the…
We study massive Dirac fields in the background of the near-horizon limit of the extremal Myers-Perry black hole in five dimensions. We consider the case in which both angular momenta have equal magnitude. The resulting Dirac equation can…
Starting from the pseudo-differential decomposition $\mathbf{D}=(-\Delta)^{\frac{1}{2}}\mathcal{H}$ of the Dirac operator $\displaystyle \mathbf{D}=\sum_{j=1}^n\mathbf{e}_j\partial_{x_j}$ in terms of the fractional operator…
In this paper we propose the hyperbolic Schredinger equation (HS). The solution of the HS for a particle in a box is obtained. It is shown that for particles with m greater of Mp the energy spectrum is independent of the mass of particle.
On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…
A concept of the total velocity that contains velocity and oscillatory velocity is proposed for the velocity solution of Dirac equation. It is shown that the electronic rest energy all comes from the oscillation of the electron itself. For…