# D. Velasco-Martínez's research while affiliated with Metropolitan Autonomous University and other places

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## Publications (5)

In this paper, we analyse the quantization of cyclotron orbits for a 2D non-relativistic and spinless charged particle under the influence of a static and uniform magnetic field, the Landau problem. We follow the algebraic approach of rising and lowering operators. The Hamiltonian is expressed in terms of the usual rising and lowering operators of...

We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest non-vanishing terms of the wave function near the...

In this paper we introduce an alternative approach to studying the evolution
of a quantum harmonic oscillator subject to an arbitrary time dependent force.
With the purpose of finding the evolution operator, certain unitary
transformations are applied successively to Schr\"odinger's equation reducing
it to its simplest form. Therefore, instead of s...

In this paper we introduce an alternative approach to studying the motion of a planar charged particle subject to a static uniform magnetic field. It is well known that an electric charge under a uniform magnetic field has a planar motion if its initial velocity is perpendicular to the magnetic field. Although some constants of motion (CsM), as the...

It is well-known that an electric charge under a uniform magnetic field has a
bidimensional motion if its initial position and velocity are perpendicular to
this magnetic field. Although some constants of motion, as the energy and
angular momentum, have been identified for this system, its features hide
others. In this work, we build generalization...

## Citations

... In response to this research question, Lu J briefly described the practical application of electromagnetic fields in science and technology, take the motion of charged particles in an electromagnetic field as an example, the close connection between technology applications and electromagnetic fields will be shown through two typical examples, students are required to conduct theoretical research on the test questions at the same time, pay more attention to the use of topic-related knowledge and the basic knowledge learned to solve practical problems [5].Gjata O to solve the motion of charged particles in compound fields, it believes that in the mutual relationship of teaching, guiding students in a timely manner, in order to enable students to learn to organize the required knowledge, that is, the integration of knowledge, in order to establish a correct spatial model, classification for processing [6]. Ibarra-Sierra V G on the movement of charged particles in the electromagnetic field, combined with the analysis of the real questions in the college entrance examination paper, discuss some motion properties and motion laws of charged particles in the electromagnetic field [7]. Aquino G preliminarily explored the teaching of the moving part of charged particles in an electric field, it involves the related motion state of charged particles in the electric field, classifies the research objects, solves problems with the help of mechanics knowledge, and expounds the use of electric field control to change the motion state of charged particles [8].Borah B K tried to use the idea of motion synthesis and decomposition through the real college entrance examination questions and their original questions, in order to deal with the complex curved motion of charged particles in the electromagnetic field, it provides some solutions for related problems [9]. ...

... For instance, large-scale vortices in the atmosphere (such as tropical cyclones) are generated by the presence of the Coriolis force. In quantum mechanics, for instance, vortexlike motion of probability fluid has been mostly investigated either in magnetic fields [10,[14][15][16][17][18][19][20][21][22][23][24] (as the magnetic component of the Lorentz force has a form similar to the Coriolis one) or in circularly polarized laser pulses [25,26]. However, it is well known that vortices can be created by disturbances that do not possess helical structures. ...

... where l B = √h /mω = √h /eB is the magnetic length. Classical electrons propagate freely along the uniform magnetic field and form confined circular orbits with radius r = √ 2l B [21,34]. The BT is a unitary transformation, and as such it preserves the commutation relations of the original operatorsâ i andâ † i . ...