Vol. 17 No. 1 Jan-Jun (2020): Revista Mexicana de Física E

The quantization method applied to the hydrogen atom involves the solution of the phase integral H pr dr = nrh, which was named by Sommerfeld as the radial quantum condition and it was solved using complex integration. In this work, we present an alternative solution to the radial quantum condition using real variable integration methods as an accessible way for students of introductory quantum mechanics courses. In addition, we show that in the Sommerfeld model the degeneracy of the energy levels is related to the geometric properties of the ellipse describing the electron motion around the nucleus.

The harmonic oscillator (HO) is present in all contemporary physics, from elementary classical mechanics
to quantum field theory. It is useful in general to exemplify techniques in theoretical physics. In this work,
we use a method for solving classical mechanic problems by first transforming them to a free particle form
and using the new canonical coordinates to reparametrize its phase space. This technique has been used to
solve the one-dimensional hydrogen atom and also to solve for the motion of a particle in a dipolar potential.
Using canonical transformations we convert the HO Hamiltonian to a free particle form which becomes
trivial to solve. Our approach may be helpful to exemplify how canonical transformations may be used in
mechanics. Besides, we expect it will help students to grasp what they mean when it is said that a problem
has been transformed into another completely different one. As, for example, when the Kepler problem is
transformed into free (geodesic) motion on a spherical surface.

A method based on a generalized function in Fourier space gives analytical solutions to homogeneous partial differential equations with constant coefficients of any order in any number of dimensions. The method exploits well-known properties of the Dirac delta, reducing the differential mathematical problem into the factorization of an algebraic expression that finally has to be integrated.  In particular, the method was utilized to solve the most general homogeneous second order partial differential equation in Cartesian coordinates, finding a general solution for non-parabolic partial differential equations, which can be seen as a generalization of d'Alambert solution.  We found that the traditional classification, i.e., parabolic, hyperbolic and elliptic, is not necessary reducing the classification to only parabolic and non-parabolic cases. We put special attention for parabolic partial differential equations, analyzing the general 1D homogeneous solution of the Photoacoustic and Photothermal equations in the frequency and time domain.  Finally, we also used the method to solve Helmholtz equation in cylindrical coordinates, showing that it can be used in other coordinates systems.

In this paper, we present a comparison of classical theory with video analysis techniques to teach kinetic and potential energy of a device with a boomerang effect as an observable and measurable concept. The device can store energy through an elastic band when it rolls down an inclined plane and can release the energy when it rolls on a horizontal surface; hence, the name Boomerang. In theoretical terms, the details of energy charge and discharge processes are analysed with Newton’s laws and Lagrangian method. The experimental results were recorded with cell phone cameras and processed with an open-source video analysis software, called ’Tracker’. The comparison shows relevant concepts about kinetic and potential energy, which can help the student to overcome some of the typical student misconceptions.

We give an elementary introduction to the Kaluza-Klein formulation, in which the gravitational and the electromagnetic fields are represented in the geometry of a five-dimensional space. We show that, in the framework of general relativity, the interaction of a point particle, or of a charged spin-zero field, with a gravitational and an electromagnetic field can be obtained through the metric of a five-dimensional space. We also show that the symmetries of the metric of this five-dimensional space lead to constants of motion for the point particles, or to operators that commute with the Klein--Gordon operator. A common misunderstanding related to the unification of gravitation and electromagnetism given by the Kaluza--Klein formulation is discussed.

One of the most powerful hurricanes that hit the Pacific coast of Mexico has been the Patricia hurricane (category five on the Saffir-Simpson scale of intensity) that occurred in 2015; the hurricane that was a genuine watershed in the mexican culture and the politics of disaster prevention in Mexico was hurricane Pauline (1997). However, even with the above, th dissemenination of knowledge about the physical phenomena that are involved in cyclogenesis and hurricane movement is very scarce, so in this paper we propose to make an introduction to the physics of hurricanes, we address the cyclogenesis theory of a hurricane, one of the most accepted theories about the behavior of its trajectories and important concepts of atmospheric sciences. The main variables that influenced Patricia and Pauline are also discuses, such as: atmospheric pressure, ocean surface temperature, wind direction and speed. Finally, an analysis is made on the formation and trajectory of Pauline and Patricia using the information shown and based on the theory presented (both in a barotropic and baroclinic framework).

The aims of teaching have evolved along with the society in which we live, from a memorial teaching to reaching one that teaches reasoning, in order to adapt to the accelerated rate of change imposed by the application of scientific discoveries in society. a society in continuous learning, which requires the ability to reason in order to adapt quickly. We are defining quality in teaching as your ability to teach reasoning. This requires developing evaluations and texts that induce reasoning. Respecting the themes of the texts of the SEP of 4th, 5th and 6th grade, changes in the presentations to children are suggested, which help the teacher so that the student understands and reasons the topics studied. Concepts on reflection, solubility, metabolism, pulleys, kaleidoscope and elasticity in in rubber bands are clarified. The teacher decides on each topic if he deduces it from previous knowledge or induces it from a demonstration or experimental data. The natural sciences are taught from the 4th year of Primary, and simple reasoning is required for children 10 to 12 years to understand them.

The Lagrangian formulation of the equations of motion for point particles is
usually presented in classical mechanics as the outcome of a series of
insightful algebraic transformations or, in more advanced treatments, as the
result of applying a variational principle. In this paper we stress two main
reasons for considering the Lagrange equations as a fundamental description
of the dynamics of classical particles. Firstly, their structure can be
naturally disclosed from the existence of integrals of motion, in a way
that, though elementary and easy to prove, seems to be less popular
--or less frequently made explicit-- than others in
support of the Lagrange formulation. The second reason is that the Lagrange
equations preserve their form in \emph{any} coordinate system --
even in moving ones, if required. Their covariant nature makes them
particularly suited to deal with dynamical problems in curved spaces or
involving (holonomic) constraints. We develop the above and related ideas in
clear and simple terms, keeping them throughout at the level of intermediate
courses in classical mechanics. This has the advantage of introducing some
tools and concepts that are useful at this stage, while they may also serve
as a bridge to more advanced courses.

Even in the most elementary courses on introductory physics at university level, the use of \textit{rotating vectors} (or \textit{phasors}) is of great help to solve problems related to alternating current circuits and to light interference. In this work I propose a novel notation to indicate a physical quantity that can be represented by a phasor. The symbolism of this new notation appears simple and easily understandable, as testified also by the outcomes of a questionnaire I distributed to students. Furthermore, the results of objective tests made on two samples of students, one trained with and the other one without the new notation, show the potential impact that the new notation can have on the understanding of phasors.

In this paper, a kinematic and dynamic model study of a robotic bicycle (Arduino Engineering Kit) is carried out to develop control algorithms for the automatic stabilization of the bicycle. The mathematical model of the bicycle is shown by the Euler-Lagrange formulation. This model allows the design and implementation of two control strategies to ensure automatic balance. The study of this dynamic system is presented as an excellent opportunity to integrate the skills acquired by students in subjects such as physics, programming, and mathematics with the purpose of designing, modeling, and controlling dynamic systems.

In this paper we search the shape of an aspherical body and the direction in space, for which the greatest deviations from the point mass
field (the difference from the inverse-square law) take place for large distances from the field source. It turns out to be a system of two equal
point-like masses at the poles of a fixed sphere (giving the greatest positive deviations from the point mass field) and uniform distribution
of point-like masses (discrete or continuous) around the sphere equator (giving the greatest negative deviations from the point mass field).
In these cases the extremal direction of the field measurement respectively passes through point-like particles and coincides with the axis of
symmetry of a ring, which is perpendicular to its plane. Our numerical estimations show that any body can be considered with reasonable
accuracy (the relative error in the determination of the field strength is less than 5%) as point-like mass if the distance to the observation
point is more than an order of magnitude larger than its characteristic sizes. The problem considered in this paper can help readers to probe
the limits of applicability of the field point source model.

The main aim of this paper is to provide a qualitative introduction to the cosmological inflation theory and its relationship with current cosmological observations. The inflationary model solves many of the fundamental problems
that challenge the Standard Big Bang cosmology such as the Flatness, Horizon and the magnetic Monopole problems. Additionally it provides an explanation for the initial conditions observed throughout the Large-Scale Structure of the Universe, such as galaxies. In this review we describe general solutions to the problems in the Big Bang cosmology carry out by a single scalar eld. Then, with the use of current surveys, we show the constraints imposed on the inflationary parameters (ns; r) which allow us to make the connection between theoretical and observational cosmology. In this way, with the latest results, it is possible to select or at least to constrain the right inflationary model, parameterized by a single scalar eld potential V (\phi).

Revista Mexicana de Física E (ISSN 1870-3542) started in 2004 as an independent spin-off publication of Revista Mexicana de Fisica (ISSN 0035-001X). It is a biannual journal devoted to publishing papers on Teaching, History and Philosophy of Physics. We have detected that the volume numbering has been erroneous from its very beginning, since this started from Volume 50 - the same number that the corresponding volume of Revista Mexicana de Fisica was carrying at that time. In order to correct for the erroneous numbering, the first volume in the year 2020 becomes Volume 17. Therefore we present hereby the following ERRATUM so as to restore the correct numbering.