Vol. 64 No. 1 Jan-Jun (2018): Revista Mexicana de Física E

Whenever we consider any relativistic quantum wave equation we are confronted with the Klein paradox, which asserts that incident particles will suffer a surplus of reflection when dispersed by a discontinuous potential. Following recent results on the Dirac equation, we propose a solution to this paradox for the Klein-Gordon case by introducing virtual beams in a natural well-posed generalization of the method of images in the theory of partial differential equations. Thus, our solution considers a global reflection coefficient obtained from the two contributions, the reflected particles plus the incident virtual particles. Despite its simplicity, this method allows a reasonable understanding of the paradox within the context of the quantum relativistic theory of particles (according to the original setup for the Klein paradox) and without resorting to any quantum field theoretic issues.

 The optical properties of an electron with an impurity in a spherical quantum dot under parabolic confinement are studied and energies, wave functions, binding energies, radial matrix elements, polarizability, susceptibility and oscillator strength have been evaluated. The numerical method used is the finite difference method in the framework of the effective mass approximation. The variation of the energy levels and radial matrix elements have been studied as function of the radius of the GaAs sphere and also as function of the frequency of the harmonic oscillator potential or parabolic potential. In addition we have studied how polarizability, susceptibility and the oscillator strength vary as a function of dot radius and at different parabolic potential frequencies.

The retarded potential, a solution of the non-homogeneous wave equation, is a subject of particular interest in many physics and engineering applications. Examples of such applications may be the problem of solving the wave equation involved in the emission and reception of a signal in a synthetic aperture radar (SAR), scattering and backscattering, and general electrodynamics for media free of magnetic charges.
However, the construction of this potential solution is based on the theory of  distributions, a topic that requires special care and time to be understood with mathematical rigor. Thus, the goal of this study is to provide an introductory analysis, with a medium level of formalism, on the construction of this potential solution and the handling of Green functions represented by sequences of well-behaved approximating
functions.

The asymptotic form of the Bel-Robinson tensor in the gravitational radiation-zone is obtained in terms of the mass quadrupole of the source.
A comparison is made with the standard formula for the gravitational power emission. The problem of a fully covariant description of gravitational radiation in terms of this tensor is briefly discussed.

In this article an analysis of original historical data is made in order to evaluate the experimental errors in Boyle’s experiment. In this evaluation, statistical regression analysis is used to estimate the constant of Boyle’s law and its uncertainty. Also is used the ideal gas law, which was established much later, as a way to evaluate this uncertainty.
This article may be useful to teachers and students as an example of using historical data in physics, and how statistical analysis can be applied to obtain information from these data.

In this paper, the solution to the Hamilton-Jacobi equation for the one-dimensional harmonic oscillator damped with the Caldirola-Kanai model is presented. Making use of a canonical transformation, we calculate the Hamilton characteristic function. It was found that the position of the oscillator shows an exponential decay similar to that of the oscillator with damping where the decay is more pronounced when increasing the damping constant γ. It is shown that when γ = 0, the behavior is of an oscillator with simple harmonic motion. However, unlike the damped harmonic oscillator where the linear momentum decays with time, in the case of the oscillator with the Caldirola-Kanai
Hamiltonian, the momentum increases as time increases due to an exponential growth of the mass m(t) = meγt.

This article presents the results of comparison of attitudes towards position of astronomy in education of students from two countries: Bosnia and Herzegovina and Croatia. A convenience sample of 396 third and fourth year high school students was surveyed using an anonymous self-report questionnaire. Students showed a certain indifference to pursuing a career in astronomy. However, both correlation and regression
analysis indicated that students manifested a high degree of interest in acquiring knowledge, experience and skills in astronomy. This bicountry study shows that students’ attitudes towards astronomy are similar considering the educational systems and position of astronomy in both Bosnia and Herzegovina and Croatia. The research results suggest that more students might consider astronomy for their scientific and
professional career provided they had more opportunities for formal education in astronomy.

Conservation of the energy and the Hamiltonian of a general non linear Schr¨odinger equation is analyzed for the finite element method “Local Discontinuous Galerkin” spatial discretization. Conservation of the discrete analogue of these quantities is also proved for the fully discrete problem using the modified Crank-Nicolson method as time marching scheme. The theoretical results are validated on a series of problems
for different nonlinear potentials.

The procedural learning is a strategy that allows improving the skills, through the reflexive exercise in diverse techniques, skills to do concrete things. In this study we provide an overview of how to implement this learning for diagnosis and improve spatial cognition in solving vector problems. Through a methodology based on design to optimize geometric skills (visualization - design-construction-transfer), following
theories of teaching - learning about levels of geometric reasoning and psychology on spatial cognition. The result of the implemented methodology showed that it is possible to improve at least one level, the geometric thinking of the students of Physics Engineering 1 of the State University of Guayaquil, according to the Van de Hiele model. Tales measurements reflected relevant facts that allowed elaborating a new instructional material to improve the academic performance of the students, through didactic techniques to improve their spatial cognitive skills.

The motion of a pendulum with a variable length is analyzed by means of a comparative Fourier and Wavelet approach. In particular Fourier and continuous Wavelet transforms have been jointly employed to investigate the non stationary signal of a variable length pendulum in an easy-to-interpret scenario addressed to undergraduate and graduate students. The comparison between the two data analysis protocols allows
to easily show that while the Fourier transform is able to extract only an average frequency value for the variable length pendulum motion, Wavelet analysis furnishes information on the time behaviour of the motion spectral content, i.e. provides a joint time-frequency analysis.

The principles underlying the theory of relativity, special and general, are presented. An easy to follow and pedagogical language is used and, based on physical examples, the motivation and some consequences of such principles are discussed. In addition, some roles of these principles when looking for a quantum gravity theory are mentioned

Free licensing software for numerical simulations, mathematics, and spectral analysis were used to explain the vibrations of a system readily available for each student in a classroom: the free beam. Its first free mode was explored analytically and experimentally, as well as using the finite element method. Prior to the course, students were unfamiliar with the usefulness of this kind of software, but after the course the students still use it. To show it, practical cases of students applying these computational tools were included at the end of this paper: a thesis about violin making, and final projects from a course in a master’s degree program. Therefore, it is evident the advantage of supporting explanations in classroom with computational tools accessible for all, and this paper can be used as tutorial for this purpose

El par electrón-hueco que surge de la teoría de semiconductores presenta un reto al usarlo como caso histórico para abordar el debate en torno al realismo científico. En este artículo presentamos y defendemos nuestra posición sobre el estatus de ese par de partículas, atendiendo a la paradoja que presentan como entidades similares desde su descripción teórica, pero profundamente diferentes desde su estatus ontológico. Para esto nos aproximamos al problema desde la perspectiva de un realismo moderado sustentado en un realismo estructural y auxiliado por conceptos en torno a la emergencia de propiedades y a la acción y puesta en operación de las entidades teóricas.