Exact Solutions Of Dirac Equation Research Articles

Exact solutions of Dirac equation for neutrinos in presence of external fields

Exact solutions of the Dirac equation in a chiral representation for neutrinos in the presence of external stresses are investigated in terms of special functions, using the algebraic method of the separation of variables in Cartesian, cylindrical, and spherical coordinates.

Bound State of a Fermion and an Extended Dyon

Investigating the bound state of fermions and extended dyons in non-relativistic as well as in relativistic frameworks, it has been shown that bound state energy eigenvalues are modified from those of fermions and point-like dyons due to the presence of massive fields in non-Abelian gauge theory. These fields play a dominating role in forming the bound state. It has also been shown that an exact solution of Dirac equation for an extended dyon-fermion system cannot be obtained, due to the presence of a term vanishing more rapidly than r−1 in the potential of this system.

DYON–DYON BOUND STATES IN NON-RELATIVISTIC AND RELATIVISTIC FRAMEWORKS

Investigating dyon–dyon bound states in non-relativistic as well as in relativistic frameworks, it has been shown that in this system a dyon moves on a cone with its apex at the other dyon and axis along its angular momentum. Dyon–dyon bound states have been investigated in a non-relativistic framework to obtain energy eigenvalue and energy eigenfunction. It has also been shown that the exact solution of Dirac equation for this system is not possible due to the presence of a term vanishing more rapidly than r-1 in the potential of the system.

DIRAC ELECTRON IN A COULOMB FIELD IN (2+1) DIMENSIONS

Exact solutions of Dirac equation in two spatial dimensions in the Coulomb field are obtained. Equation which determines the so-called critical charge of the Coulomb field is derived and solved for a simple model.

Some exact solutions of the Dirac equation in gravitational fields

Some exact solutions of the general covariant Dirac equation in gravitational fields, namely in constant curvature de Sitter spacetime and in Milne's Universe are obtained. The tetrads for both cases are constructed on the basis of global quasi-Cartesian coordinates that allow one to exclude coordinate effects connected with the rotation of the local frame under the transition of the triad from one spacetime point to another. Solutions in the form of a spherical bispinor wave with time amplitude modulation are demonstrated for both cases of gravitational fields and the possibility of analogical solutions in the form of cylindrical and plane spinor waves for the de Sitter spacetime is discussed. All the solutions are obtained by means of the algebraic method of separation of variables.

BOUND STATES OF THE DIRAC EQUATIONS WITH HULTHéN-TYPE POTENTIALS

The exact solutions of bound states of Dirac equation with one-dimensional vector and scalar Hulthén-type potential are obtained. For three-dimensional Hulthén-type potential, the S-wave exact solutions of Dirac equations are also presented provided the scalar potential is equal to the vector potential.

Exact solutions of Dirac equation

In this paper Dirac equation for two electromagnetic potentials viz vector potential and scalar potential have been solved. These solutions of the Dirac equation are written in terms of known solutions of the Schrodinger equation. The presentation is within the two-component relativistic description. Mainly the bound state solutions have been obtained.

The spin kinematics for a charged particle in a uniform magnetic field

The influence of a uniform magnetic field on the spin orientation of electrons in a beam is calculated according to the Dirac theory. It is shown that, when the field is perpendicular to the electron beam path, the spin orientation does not change with respect to the direction of propagation. The calculations are performed using the exact solution of Dirac equation.