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Papers by Víctor Villalba
physica status solidi (b), 1999
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. Wit... more 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 generalization 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.
Progress of Theoretical Physics, 1993
In this article the particle creation process of scalar and spin 1/2 particles in a spatially ope... more 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 with radiation and dustlike matter is analyzed. The Klein-Gordon and the Dirac equations are solved via separation of variables. After comparing the in and out vacua, we obtain that the number of created particles corresponds to Planckian and Fermi-Dirac distributions for the scalar and Dirac cases respectively. § 1. Introduction
Physics Letters A, 1994
In the present article we analyze the bound states of an electron in a Coulomb field when an Ahar... more 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.
Modern Physics Letters A, 1993
In this letter we solve, via separation of variables, the massless Dirac equation in a nonstation... more In this letter 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.
Physics Letters A, 1998
We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger equations for a two-dimension... more We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger 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.
Modern Physics Letters A, 2002
In this article we compute the density of Dirac particles created by a cosmological anisotropic B... more In this article we compute the density of Dirac particles created by a cosmological anisotropic Bianchi I universe in the presence of a constant electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.
Physics Letters A, 2006
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spati... 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.
The European Physical Journal C, 2009
Journal of Mathematical Physics, 1993
In the present article exact solutions of the Dirac equation for electric neutral particles with ... more In the present article exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments are presented. 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.
Physica E: Low-dimensional Systems and Nanostructures, 2001
We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativ... more We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.
Modern Physics Letters B, 2003
We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Co... more We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis variational method we compute the wave function and the energy level and show how it depends on the magnetic field strength. We compare the results with those obtained numerically as well as in the non-relativistic limit.
Journal of Physics: Condensed Matter, 1996
ABSTRACT
Journal of Physics: Condensed Matter, 2001
We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact ... more We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schrödinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those obtained by using an accurate numerical technique, showing that the relative error is reasonably small, although the first method consistently underestimates the correct values. The approximate groundstate Hartree-Fock and local-density Kohn-Sham energies, estimated using the shifted-1/N method, are compared with accurate numerical self-consistent solutions. We make some perturbative analyses of the exact energy in terms of the confinement strength, and we propose some interpolation formulae. Similar analysis is made for both mean-field approximations and interpolation formulae are also proposed for these exchange-only ground-state cases.
Physical Review A, 2005
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon pot... more We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zeroreflection condition depends on the shape of the potential.
physica status solidi (b), 1999
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. Wit... more 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 generalization 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.
Progress of Theoretical Physics, 1993
In this article the particle creation process of scalar and spin 1/2 particles in a spatially ope... more 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 with radiation and dustlike matter is analyzed. The Klein-Gordon and the Dirac equations are solved via separation of variables. After comparing the in and out vacua, we obtain that the number of created particles corresponds to Planckian and Fermi-Dirac distributions for the scalar and Dirac cases respectively. § 1. Introduction
Physics Letters A, 1994
In the present article we analyze the bound states of an electron in a Coulomb field when an Ahar... more 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.
Modern Physics Letters A, 1993
In this letter we solve, via separation of variables, the massless Dirac equation in a nonstation... more In this letter 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.
Physics Letters A, 1998
We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger equations for a two-dimension... more We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger 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.
Modern Physics Letters A, 2002
In this article we compute the density of Dirac particles created by a cosmological anisotropic B... more In this article we compute the density of Dirac particles created by a cosmological anisotropic Bianchi I universe in the presence of a constant electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.
Physics Letters A, 2006
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spati... 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.
The European Physical Journal C, 2009
Journal of Mathematical Physics, 1993
In the present article exact solutions of the Dirac equation for electric neutral particles with ... more In the present article exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments are presented. 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.
Physica E: Low-dimensional Systems and Nanostructures, 2001
We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativ... more We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.
Modern Physics Letters B, 2003
We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Co... more We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis variational method we compute the wave function and the energy level and show how it depends on the magnetic field strength. We compare the results with those obtained numerically as well as in the non-relativistic limit.
Journal of Physics: Condensed Matter, 1996
ABSTRACT
Journal of Physics: Condensed Matter, 2001
We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact ... more We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schrödinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those obtained by using an accurate numerical technique, showing that the relative error is reasonably small, although the first method consistently underestimates the correct values. The approximate groundstate Hartree-Fock and local-density Kohn-Sham energies, estimated using the shifted-1/N method, are compared with accurate numerical self-consistent solutions. We make some perturbative analyses of the exact energy in terms of the confinement strength, and we propose some interpolation formulae. Similar analysis is made for both mean-field approximations and interpolation formulae are also proposed for these exchange-only ground-state cases.
Physical Review A, 2005
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon pot... more We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zeroreflection condition depends on the shape of the potential.