Vol. 20 No. 1 Jan-Jun (2023): Revista Mexicana de Física E
REVISTA MEXICANA DE FÍSICA E, year 20, issue 1, January-June 2023. Semiannual Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf-e, rmf@ciencias.unam.mx. Chief Editor: Alfredo Raya Montaño. INDAUTOR Certificate of Reserve: 04-2022-111014105800-203, e-ISSN: 2683-2216, granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 13, 2023.
02 Education in Physics
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Solution of the coupled β functions of the Standard Model and its minimal supersymmetric extension
Abstract:⬇️ Scroll down to see the full summaryThe Standard Model contains three coupling constants α1, α2 and α3 associated to the intern symmetry groups. However, even such constants are named like that, in fact they are not, they are energy dependent functions. The functional form of the evolution satisfies a set of coupled differential equations the coupled β functions. In general these β functions are highly coupled, from this arises the necessity of using numerical methods for the solution of the problem, because it is not possible to obtain it analytically. In this work it is used the adaptive Runge-Kutta method for a set of ordinary differential equations. The physical motivation of this work arise from the fact that the coupling constants α1, α2 and α3 are associated to the electromagnetic interaction, the weak interaction and the strong interaction, respectively. In the Standard Model, the solutions for α1 and α2 intersect in a point, which can be interpreted as a unification of two fundamental interactions exists. Nevertheless, using the minimal supersymmetric extension of the Standard Model, the three coupling constants intersect in a region, reaching what is known as the Grand Unification.
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Socio-scientific issues in physics learning to improve students’ critical thinking skills
Abstract:⬇️ Scroll down to see the full summarySocio Scientific Issues (SSI) is a social issue that causes controversy and can be studied based on scientific facts. Applying SSI to physics subjects helps students relate physics to real things in everyday life. The purpose of this study was to determine the teacher's view of the success of students' critical thinking processes that can be obtained from studying physics through SSI. The research method used is a qualitative method with a phenomenological approach. This study involved 4 resource persons consisting of 2 senior and 2 junior physics teachers. The results of this study indicate that SSI in physics learning can help students practice critical thinking skills. This is based on the various processes experienced by students during the physics learning process with SSI.
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A Python program to draw energy level diagram and to calculate quantum defects, the high lying Rydberg level
Abstract:⬇️ Scroll down to see the full summaryRydberg atoms have strong and adjustable atomic interactions that can be tweaked by choosing different states with various principal quantum numbers or orbital angular momentum. They are highly used in quantum information applications. Furthermore, these atoms have long lifetimes and many possible energy levels, and their separations enable coupling to electromagnetic fields with frequencies ranging over six orders of magnitude. We studied some properties of these atoms and have developed a python program; the program gives two options. Firstly, it calculates energies of elements in s, p, d, and f orbitals and draws an energy level diagram of the element listed in the program. Secondly, it gives an option for calculating energy and quantum defects of atoms and ions, either listed or not listed in the program and generates their graphs accordingly. There are 21 elements in the database whose energy level diagrams could be drawn. The database can be extended by adding more elements.
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Application of the double numbers in the representation of the Lorentz transformations
Abstract:⬇️ Scroll down to see the full summaryWe show that the orthochronous proper Lorentz transformations that leave one of the Cartesian coordinates fixed can be represented by $2 \times 2$ unitary matrices with determinant equal to 1, whose entries are double numbers. This representation is employed in the calculation of the Wigner angle, which arises in the composition of two boosts in arbitrary directions.
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Ground state energy of the hydrogen atom inside penetrable spherical cavities; variational approach
Abstract:⬇️ Scroll down to see the full summaryIn this work we calculate the ground state energy of the hydrogen atom confined in a sphere of penetrable walls of radius Rc. Inside the sphere the system is subject to a Coulomb potential, whereas outside of it the potential is a finite constant V0. The energy is obtained as a function of Rc and V0 by means of the Rayleigh-Ritz variational method, in which, the trial function is proposed as a free particle wave function within a finite square well potential but including an exponential factor that takes into account the electron-nucleus Coulomb attraction. For an impenetrable sphere, , the energy grows fast as Rc approaches zero. On the other hand, when the height of the barrier V0 is finite, the energy increases slowly as Rc goes to zero. We also compute the Fermi contact term, nuclear magnetic screening, polarizability, pressure and tunneling as a function of Rc and V0. As expected, these physical quantities approach the corresponding values of the free hydrogen atom as Rc grows. We also discuss the pressure-induced ionization of the hydrogen atom. The present results are found in good agreement with those previously published in the literature.
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Mínimos cuadrados para la calibración en reconstrucción 3D mediante proyección de franjas
Abstract:⬇️ Scroll down to see the full summaryIn surface measurement systems using the phase shift technique with fringe projection, the calibration of the system is essential to determine the relation between obtained phase and real height of the object. In this work, we present a detailed mathematical analysis for the linear calibration model. Derivation of the least squares scheme which is required for data estimation, is developed intuitively by means of using the underlying theory in numerical analysis. The calibration method is applied to the surface of a 3D object obtaining remarkable results.
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Lambda-shiftings for the secondary sources in the Young's experiment allow to rebuild patterns look like piston/tilt
Abstract:⬇️ Scroll down to see the full summaryIn this work, we perform the mathematical theory used by Born and Wolf to rebuild a geometric characterization for piston and tilt or a combination of both surface errors by shifting the secondary sources in the classical Young's experiment. The last is accomplished making a comparison between the generated patterns of classical Young' experiment and Young's patterns when the secondary sources are shifted axially of the order of $\lambda$. Images with effects looks like to surface errors by piston or tilt are obtained and this give us a good idea on how could be the co-phasing of an optical flat surface in a real experiment.
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GUI of vector analysis on spreadsheets for students and teachers
Abstract:⬇️ Scroll down to see the full summaryA Graphical User Interface (GUI) teaching tool to teach different vectors modules to college and undergraduate students have been developed. The Physics and Mathematics students can benefit from these executable spreadsheets for practicing vector algebra with minimum inputs and through diagrams and answers as output. The spreadsheets are employed to calculate vectors resolution, addition, projection, and multiplication because they are ubiquitous. Some GUI on vectors available online gives the results, whereas this GUI shows the calculation steps to reach the results, which helps learn the subject effectively. The developed GUI also assists the mentors regarding their lab work and exams to make different papers with answer keys.
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Estudio de la actividad ´optica de sustancias org´anicas
Abstract:⬇️ Scroll down to see the full summaryOptical rotatory power found in certain organic substances is a phenomenon consequence of optical activity, that is, of the interaction between an electromagnetic field and the structure of particular molecules. Consequently, it is a topic of interest from the physics and chemistry perspectives, a situation relevant for the academic formation of students, broadening their vision outside academic physics. This paper details how to carry out an experimental activity that allows a quantitative analysis for calculating the rotational power of basic chemical compounds, easy to obtain or produce in a teaching laboratory. The results found for the optical rotation of the studied substances have an average error of 10 % with respect to the reported values; however, it is also possible to deduce when a substance is not pure since the error with respect to the reported values increases.
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A new rolling friction coefficient measurement method based on the work-energy theorem
Abstract:⬇️ Scroll down to see the full summaryThe rolling friction coefficient represents a characteristic parameter for the rolling motion. To determine the rolling friction coefficient, we propose a simple method based on the conservation of energy. The measuring setup includes the tools and materials that are simple and easy to obtain, such as the spring, ruler, and a small laboratory wheeled cart. In this paper, we have determined the rolling friction coefficient for several masses of the test carts and different lengths of spring compression. When the spring is compressed, its energy is directly proportional to the square of the length of the spring compression. The initial speed of the cart was determined using the law of energy conservation, and the length that the cart goes before stopping is measured with a ruler. The conclusion is that the value of the rolling friction coefficient is usually very small and that the mass of an object will affect the friction force but will not affect the rolling friction coefficient. Besides determining the rolling friction coefficient, this technique should help students comprehend the concept of friction easily.
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The entropy of systems
Abstract:⬇️ Scroll down to see the full summaryThe entropy concept is studied from the perspective of several formalisms. It is reviewed the origins of this in the classical thermodynamics. It also is developed a step-by-step-clearly demonstration about it. After that, it is connected this formula with the entropy of Shannon. Elementary concepts of the quantum mechanics are explained to demonstrate the von Neumann entropy formula. It is proposed the entropy concept as a measure of the variability into the distribution of the states of a system given a set of rules that operate inside it for a while. From the perspective of the information theory, a language reaches a configuration to be optimal for communications. In this way, systems and languages can be studied using the same concept of entropy. It is stressed the importance of the teaching of the entropy because this is useful in the development of new technologies, for example the quantum communications.
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Determinación de las concentraciones al equilibrio en una reacción química
Abstract:⬇️ Scroll down to see the full summaryIn this work, the problem of the computation of equilibrium concentrations of a chemical reaction is discussed, when higher than second order polynomial equations are involved. This situation depends on the number of reactants and products of the chemical reaction, as well as its stoichiometric coefficients. Despite this being a frequent case, the problem is not addressed in introductory chemical and physical chemistry textbooks, since the equations must be solved numerically. In this manuscript, three programs are provided for the bisection, Newton-Raphson and secant numerical methods. These codes can be easily utilized for reactions involving up to seven reactants and seven products. The iterative methods are explained in detail with the explicit intention of preventing their use as black boxes. In this way, this constitutes an interesting application from physical chemistry for students of Mathematics, while it is a didactical exposition to the numerical solution of non-linear equations for students of Physics, Chemistry and Engineering. The example provided can also be used in numerical methods courses. Finally, the performance of the three methods is discussed using as an example the Haber-Bosch process. No installations on devices are required in order to execute the codes.
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The one-dimensional Coulomb oscillator
Abstract:We consider the one-dimensional oscillations of a charged point particle under the restoring Coulomb force. We find that, for very small amplitudes, the speed of the particle remains almost constant. We also obtain the exact analytical expression for finding the oscillation period. It turns out to be a monotonically increasing function of the amplitude. For small amplitudes, this quantity is directly proportional to the amplitude itself.⬇️ Scroll down to see the full summary -
Retarded potentials and radiation of a rotating charged rod
Abstract:⬇️ Scroll down to see the full summaryIn this paper we determine the electromagnetic properties of a rotating charged rod, which rotates around the x-axis with an angular frequency that it’s not constant. As the charge is changing its position over time, the electromagnetic information reaches us with a certain time lag. Therefore, it is necessary to obtain the time-dependent(retarded) potentials at any point in space, for which we need multipolar expansion to determine the field at any point in space and do a Taylor expansion of the distance at which we want to measure the electromagnetic fields, in the static and induction zone. Then, we determine the Poynting vector in the corresponding radiation zone. Finally, we determine the radiated power, emphasizing the symmetries of the problem and showing how we can approach its solution considering these symmetries.
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