We apply the algebraic method of separation of variables in order to reduce the Dirac equation to a set of coupled first-order ordinary differential equations. We obtain the sufficient conditions for partial or complete separability... more
We apply the algebraic method of separation of variables in order to reduce the Dirac equation to a set of coupled first-order ordinary differential equations. We obtain the sufficient conditions for partial or complete separability corresponding to homogeneous cosmological backgrounds.
Research Interests:
Research Interests:
In the present article we revisit the problem of a relativistic Dirac electron. Using a second order formalism which reduces the problem of finding the energy spectrum to solving the Whittaker equation, we show that the only physical... more
In the present article we revisit the problem of a relativistic Dirac electron. Using a second order formalism which reduces the problem of finding the energy spectrum to solving the Whittaker equation, we show that the only physical solution is obtained by truncating the hypergeometric series. Therefore the energy spectrum does not depend on any free parameters for 119 < Z < 137. RESUMEN. En el presente articulo se estudia el problema de un electron relativista de Dirac. Haciendo uso de un formalismo de segundo orden que reduce el problema de encontrar el espectro de energia a resolver la ecuacion de vVhittaker, se muestra que la unica solucion fisicamente aceptable se obtiene truncando la serie hipergeometrica. Por consiguiente, el espectro de energia no depende de ningun parametro libre para 119 < Z < 137.
Research Interests: Physics and Hydrogen Atom
Research Interests:
Research Interests:
Research Interests:
Research Interests: Materials Engineering, Physics, Condensed Matter Physics, Nanotechnology, Quantum Dots, and 9 moreTheoretical Condensed Matter Physics, Electronic Structure, Hartree fock method, Schroedinger Equation, Quantum Dot, Local Density Approximation, Mean Field Approximation, Perturbation Theory, and energy spectrum
Research Interests:
We obtain exact solutions of the Klein-Gordon and Pauli Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular... more
We obtain exact solutions of the Klein-Gordon and Pauli Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states.
Research Interests:
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are... more
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are explicitly obtained up to fifth order of the phase-integral approximation. As in previous reports [1-3], we point out that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.
We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary... more
We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary time-dependence of the field, we discuss the asymptotic behavior of the solutions with the help of the relativistic Hamilton-Jacobi equation.
Research Interests: Mathematics, Mathematical Physics, Field Theory, Physics, General Relativity, and 11 moreEarly Universe, Magnetic field, Open University, Mathematical Sciences, Relativity and Gravitation, Physical sciences, Dirac equation, Time Dependent, Separation of variables, Hamilton Jacobi equation, and Exact solution methods
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is... more
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.
Research Interests:
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in... more
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms of parabolic cylinder functions and showing explicitly how the resonant behavior depends on the sign and strength of the electric field, we derive an approximate expression for the value of the resonance energy in terms of the electric field and delta interaction strength.
Research Interests:
We solve the two-component Dirac equation in the presence of a spatially one-dimensional symmetric cusp potential. We compute the scattering and bound state solutions and we derive the conditions for transmission resonances as well as for... more
We solve the two-component Dirac equation in the presence of a spatially one-dimensional symmetric cusp potential. We compute the scattering and bound state solutions and we derive the conditions for transmission resonances as well as for supercriticality.
Research Interests:
Research Interests:
Research Interests:
In this paper the separation of variables is presented in the Dirac equation in open, flat, and closed expanding cosmological Robertson-Walker universes. The equations governing the radial variable and the evolution of the time-dependent... more
In this paper the separation of variables is presented in the Dirac equation in open, flat, and closed expanding cosmological Robertson-Walker universes. The equations governing the radial variable and the evolution of the time-dependent factor are obtained. An exact solution to the Weyl equation is derived for an arbitrary expansion factor of the Robertson-Walker metrics. An exact solution to Dirac equation in a universe filled with radiation is also presented.
Research Interests: Mathematical Physics, Mathematical Sciences, Physical sciences, Symmetry, Dirac equation, and 11 moreSpace Time, PARTIAL DIFFERENTIAL EQUATION, Wave Equation, Time Dependent, Separation of variables, Differential equation, Orthogonal Transformation, Elementary Particles, Ordinary Differential Equation, Exact solution methods, and Charged Particles
In this article we obtain, by separation of variables, an exact solution to the Klein–Gordon and Dirac equations in a cosmological, spatially-closed, Robertson–Walker space-time with a positive cosmological constant Λ. The model is... more
In this article we obtain, by separation of variables, an exact solution to the Klein–Gordon and Dirac equations in a cosmological, spatially-closed, Robertson–Walker space-time with a positive cosmological constant Λ. The model is associated with a universe filled with radiation. We analyze the phenomenon of particle creation for different values of the dimensionless coupling constant ξ.
Research Interests:
In the present article we study the energy levels of a 2D hydrogenic atom when a constant magnetic field is applied. We compute the energy spectrum with the help of a generalization of the mesh point technique recently proposed by... more
In the present article we study the energy levels of a 2D hydrogenic atom when a constant magnetic field is applied. We compute the energy spectrum with the help of a generalization of the mesh point technique recently proposed by Schwartz. We also estimate, via a variational method, the upper energy bound for small and large values of the external
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
ABSTRACT
Research Interests:
Research Interests:
Research Interests:
ABSTRACT
ABSTRACT
Research Interests:
Research Interests:
Research Interests:
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are... more
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are explicitly obtained up to fifth order of the phase-integral approximation. As in previous reports [1-3], we point out that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.
Research Interests:
Motivated by seeking kinetic origins for seedsof the large-scale structure formation in the universe,we investigate the properties of a generalizedaxisymmetric Bianchi IX type model. Such a model, which is supposed to describe... more
Motivated by seeking kinetic origins for seedsof the large-scale structure formation in the universe,we investigate the properties of a generalizedaxisymmetric Bianchi IX type model. Such a model, which is supposed to describe non-interactingradiation of dust-like matter posterior to decoupling,has the advantage ofbehaving asymptotically as a closefrw model with a cosmological constant. It shows avanishing vorticity, a decreasing shear of matter
Research Interests:
ABSTRACT The scattering of a relativistic electron by an infinite solenoid, of finite radius, is analysed. The relativistic correction and the spin polarization contributions to the scattering amplitude are obtained.