Related papers: Dirac equation: the stationary and dynamical scatt…
The classical equation of motion of a charged point particle, including its radiation reaction, is described by the Lorentz-Dirac equation. We found a new class of solutions that describe tunneling (in a completely classical context!). For…
This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.
An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…
Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
Starting with the Dirac equation outside the event horizon of a non-extreme Kerr black hole, we develop a time-dependent scattering theory for massive Dirac particles. The explicit computation of the modified wave operators at infinity is…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
By requiring unambiguous symmetric quantization leading to the Dirac equation in a curved space, we obtain a special representation of the spin connections in terms of the Dirac gamma matrices and their space-time derivatives. We also…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
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…
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…
This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…
We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially…
By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac's theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a…
In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum pu with its alternative p_u+mwbf_u(x_u)). In particular, the quantum dynamics is considered for the function f_u(x_u) to be…
It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the…
In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the…
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…
The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in…
Hidden symmetry in Coulomb interaction is one of the mysterious problems of modern physics. Additional conserved quantities associated with extra symmetry govern wide variety of physics problems, from planetary motion till fine and…