arXiv subjects
Publications and source records attributed to Victor M. Villalba.
In the present article we analyze the phenomenon of particle creation in a cosmological anisotropic universe when a constant electric field is present. We compute, via the Bogoliubov transformations, the density number of particles created.
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a genera lization of virial theorem, which consists in scaling the wave function, we calculate the binding energies of the 1S, $2P^-$ and $3D^-$ levels. We compare the computed energy spectra with those obtained via a generalization of the mesh point technique as well as the shifted 1/N method. We show that the variational solutions present a very good behavior in the weak and strong magnetic field regimes.
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method, we calculate the energy eigenvalues of the 1S, 2P- and 3D- levels. We compare the computed energy spectra with those obtained via a generalization of the mesh point technique as well as the shifted 1/N method. We show that the variational solutions present a good behavior in the weak and strong magnetic field regimes.
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.
In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schrödinger equation in spherical coordinates and we show how the Hydrogen energy spectrum depends on the Aharonov-Bohm and the magnetic monopole strengths. In passing, the Klein-Gordon equation is solved.
The Dirac equation in spherically symmetric fields is separated in two different tetrad frames. One is the standard cartesian (fixed) frame and the second one is the diagonal (rotating) frame. After separating variables in the Dirac equation in spherical coordinates, and solving the corresponding eingenvalues equations associated with the angular operators, we obtain that the spinor solution in the rotating frame can be expressed in terms of Jacobi polynomials, and it is related to the standard spherical harmonics, which are the basis solution of the angular momentum in the Cartesian tetrad, by a similarity transformation.
In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle.
In the present article we solve, via separation of variables, the massless Dirac equation in a nonstationary rotating, causal Gödel-type cosmological universe, having a constant rotational speed in all the points of the space. We compute the frequency spectrum. We show that the spectrum of massless Dirac particles is discrete and unbounded.
In the present article we present exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments. Using the algebraic method of separation of variables, the Dirac equation is separated in cartesian, cylindrical and spherical coordinates, and exact solutions are obtained in terms of special functions.
In this article the particle creation process of scalar and spin 1/2 particles in a spatially open cosmological model associated with a universe filled by radiation and dustlike matter. The Klein-Gordon and Dirac equations are solved via separation of variables. After comparing the{\it \ in }and% {\it \ out} vacua, we obtain that the number of created particles corresponds to Planckian and Fermi-Dirac distributions for the scalar and Dirac cases