cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.14326538
title: Conformal mapping as an aid for solving problems in physics

description: Most of the relevant physics problems involve differential equations. A special class of problems is those that involve second-order partial differential equations. The Laplace equation, for example, is fundamental in electrostatics, fluid dynamics, and thermodynamics. In many cases, obtaining the solution to the Laplace equation is difficult with the frequently used methods, namely: separation of variables and the method of images. In this work, we will present the conformal transformations as an additional tool that, in certain cases, is much simpler to use. As this tool is often overlooked in regular exact courses, our goal is to help fill this gap by presenting a didactic, introductory, and an easily understood text to the interested public.
DOI: 10.6084/m9.figshare.14326538.v1
title: Conformal mapping as an aid for solving problems in physics

description: Most of the relevant physics problems involve differential equations. A special class of problems is those that involve second-order partial differential equations. The Laplace equation, for example, is fundamental in electrostatics, fluid dynamics, and thermodynamics. In many cases, obtaining the solution to the Laplace equation is difficult with the frequently used methods, namely: separation of variables and the method of images. In this work, we will present the conformal transformations as an additional tool that, in certain cases, is much simpler to use. As this tool is often overlooked in regular exact courses, our goal is to help fill this gap by presenting a didactic, introductory, and an easily understood text to the interested public.
DOI: 10.6084/m9.figshare.14326541.v1
title: Divergent Integrals Treatment in Quantum Field Theory

description: This paper presents a brief review on regularization methods and shows that the combination of two techniques could preserve symmetries in all orders of the Perturbation Theory. We will see, with two simple examples in the one-loop-order, what a regularization method needs to preserve symmetries. Furthermore, it will be shown that the problems with symmetry violations by regularization methods are related to the consequences of not being able to simply shift a variable in these divergent integrals. To facilitate the analysis between methods and provide analytical expressions for the finite parts of amplitudes, it was systematized in terms of a set of special functions. In the Appendix we introduce these functions and then cases of specific interest, functions continuity and some useful limits will be presented.
DOI: 10.6084/m9.figshare.14326541
title: Divergent Integrals Treatment in Quantum Field Theory

description: This paper presents a brief review on regularization methods and shows that the combination of two techniques could preserve symmetries in all orders of the Perturbation Theory. We will see, with two simple examples in the one-loop-order, what a regularization method needs to preserve symmetries. Furthermore, it will be shown that the problems with symmetry violations by regularization methods are related to the consequences of not being able to simply shift a variable in these divergent integrals. To facilitate the analysis between methods and provide analytical expressions for the finite parts of amplitudes, it was systematized in terms of a set of special functions. In the Appendix we introduce these functions and then cases of specific interest, functions continuity and some useful limits will be presented.
DOI: 10.6084/m9.figshare.14326544
title: Larmor’s power of a charged particle under the effect of an electric field generated by two homogeneously charged dielectric disks

description: In this article, we investigate the dynamics of a charged particle when subjected to an electric field generated by two dielectric and homogeneous disks. We analyzed the construction of the motion equation for the accelerated charge, which in the linear approximation of the electric force results in a Simple Harmonic Oscillator (SHO). Subsequently, the Abraham-Lorentz radiation force is incorporated into the motion equation because the accelerated movement of the load results in the emission of energy radiation and, in this situation, behaves like a Damped Harmonic Oscillator (DHO). And we calculated Larmor’s radiation power for this damped particle motion.
DOI: 10.6084/m9.figshare.14326544.v1
title: Larmor’s power of a charged particle under the effect of an electric field generated by two homogeneously charged dielectric disks

description: In this article, we investigate the dynamics of a charged particle when subjected to an electric field generated by two dielectric and homogeneous disks. We analyzed the construction of the motion equation for the accelerated charge, which in the linear approximation of the electric force results in a Simple Harmonic Oscillator (SHO). Subsequently, the Abraham-Lorentz radiation force is incorporated into the motion equation because the accelerated movement of the load results in the emission of energy radiation and, in this situation, behaves like a Damped Harmonic Oscillator (DHO). And we calculated Larmor’s radiation power for this damped particle motion.
DOI: 10.6084/m9.figshare.14326546.v1
title: Group theory and the role of symmetries in physics

description: This paper sets out to present, in a brief and intuitive way, fundamental aspects of group theory, establishing its relation with the idea of symmetry, drawing a parallel with the development of quantum mechanics and particle physics. We try to approach this topic, which is frequently neglected in undergraduate courses, always starting from the concept of invariance of a given quantity of interest to, only after that, introduce the idea of a symmetry group.
DOI: 10.6084/m9.figshare.14326546
title: Group theory and the role of symmetries in physics

description: This paper sets out to present, in a brief and intuitive way, fundamental aspects of group theory, establishing its relation with the idea of symmetry, drawing a parallel with the development of quantum mechanics and particle physics. We try to approach this topic, which is frequently neglected in undergraduate courses, always starting from the concept of invariance of a given quantity of interest to, only after that, introduce the idea of a symmetry group.
DOI: 10.6084/m9.figshare.14326549
title: Ladder Operators for the Spherical 3D Harmonic Oscillator

description: The Schrödinger equation for an isotropic three-dimensional harmonic oscillator is solved using ladder operators. The starting point is the shape invariance condition, obtained from supersymmetric quantum mechanics. Generalized ladder operators can be constructed for the three spherical spatial coordinates. Special emphasis is given to the adaptation made to each of these coordinates. The approach used is general and is indicated as an alternative method to solve the Schrödinger equation.
DOI: 10.6084/m9.figshare.14326549.v1
title: Ladder Operators for the Spherical 3D Harmonic Oscillator

description: The Schrödinger equation for an isotropic three-dimensional harmonic oscillator is solved using ladder operators. The starting point is the shape invariance condition, obtained from supersymmetric quantum mechanics. Generalized ladder operators can be constructed for the three spherical spatial coordinates. Special emphasis is given to the adaptation made to each of these coordinates. The approach used is general and is indicated as an alternative method to solve the Schrödinger equation.
DOI: 10.6084/m9.figshare.14326550.v1
title: The equivalence principle involving electric charges: Rohrlich’s contribution for the discussion on that classical problem

description: The equivalence principle is a fundamental concept of the general relativity and it essentially express the equality between inertial and gravitational mass. The idealizations concerning the so-called “Einstein elevator” containing observers and test masses enable us to readily understand such a concept, however the scenario becomes more complex when there are electric charges involved because they emit radiation when accelerated. Hastily, we could claim that a resting charge in a gravitational field does not radiate, while another inside an accelerated elevator relatively to an inertial frame of reference does emit radiation, seemingly violating the equivalence principle. Such a problem has stirred up many discussions and we present here the analysis put forth by Fritz Rohrlich in the 1960s. The author shows that the electromagnetic field of an accelerated charge has radiative form for some frames of reference only, thereby such a phenomenon does not have an absolute nature. The approach is simple and it defines the spacetime curvature as being null in the domain, and therefore it does not in fact represent a solution for the apparent paradox (once it does not consider a real gravitational field); however, its results have a didactic interest once they are useful as a motivation for a more profound discussion and help us to understand that there is no incompatibility between the equivalence principle and electrical charges. Also, the discussion shown here may be used as a starting point for more recent and general works on the problem.
DOI: 10.6084/m9.figshare.14326550
title: The equivalence principle involving electric charges: Rohrlich’s contribution for the discussion on that classical problem

description: The equivalence principle is a fundamental concept of the general relativity and it essentially express the equality between inertial and gravitational mass. The idealizations concerning the so-called “Einstein elevator” containing observers and test masses enable us to readily understand such a concept, however the scenario becomes more complex when there are electric charges involved because they emit radiation when accelerated. Hastily, we could claim that a resting charge in a gravitational field does not radiate, while another inside an accelerated elevator relatively to an inertial frame of reference does emit radiation, seemingly violating the equivalence principle. Such a problem has stirred up many discussions and we present here the analysis put forth by Fritz Rohrlich in the 1960s. The author shows that the electromagnetic field of an accelerated charge has radiative form for some frames of reference only, thereby such a phenomenon does not have an absolute nature. The approach is simple and it defines the spacetime curvature as being null in the domain, and therefore it does not in fact represent a solution for the apparent paradox (once it does not consider a real gravitational field); however, its results have a didactic interest once they are useful as a motivation for a more profound discussion and help us to understand that there is no incompatibility between the equivalence principle and electrical charges. Also, the discussion shown here may be used as a starting point for more recent and general works on the problem.
DOI: 10.6084/m9.figshare.14326553
title: Law of reflection, Snell’s law and the Goos-Hänchen effect: an approach from a corpuscular model of light

description: In this article we use Einstein’s model that treats light in its corpuscular behavior to determine the laws of reflection and refraction. For total internal reflection we predict the Goos-Hanchen shift.
DOI: 10.6084/m9.figshare.14326553.v1
title: Law of reflection, Snell’s law and the Goos-Hänchen effect: an approach from a corpuscular model of light

description: In this article we use Einstein’s model that treats light in its corpuscular behavior to determine the laws of reflection and refraction. For total internal reflection we predict the Goos-Hanchen shift.
DOI: 10.6084/m9.figshare.14326555
title: Temporal evolution of the distribution function of one-dimensional systems

description: Phase space dynamics plays an important role in systems of many particles that move towards equilibrium. In this work, we study such dynamics in some one-dimensional systems: (i) non-linear and non-interacting pendulums; and (ii) many particles interacting gravitationally. The temporal evolution of systems with many particles, in a non-collisional regime, is governed by the Vlasov equation, which we solve numerically. The original equations are separated into transport equations via Lie’s splitting method. The positive and flux conservative numerical method is used, with a monotonized central-difference (MC) slope limiter. Although we present solutions to common problems in the area, detailed discussions are not frequent. Soon this work can be explored in the teaching of physics.
DOI: 10.6084/m9.figshare.14326555.v1
title: Temporal evolution of the distribution function of one-dimensional systems

description: Phase space dynamics plays an important role in systems of many particles that move towards equilibrium. In this work, we study such dynamics in some one-dimensional systems: (i) non-linear and non-interacting pendulums; and (ii) many particles interacting gravitationally. The temporal evolution of systems with many particles, in a non-collisional regime, is governed by the Vlasov equation, which we solve numerically. The original equations are separated into transport equations via Lie’s splitting method. The positive and flux conservative numerical method is used, with a monotonized central-difference (MC) slope limiter. Although we present solutions to common problems in the area, detailed discussions are not frequent. Soon this work can be explored in the teaching of physics.
DOI: 10.6084/m9.figshare.14326558.v1
title: Dissipative Dynamics and Uncertainty Measures of a Charged Oscillator in the Presence of the Aharonov-Bohm Effect

description: We analyze the effects of dissipation in a charged oscillator in the presence of the Aharonov-Bohm effect by using time-dependent mass (m(t)) Hamiltonians. We consider two different models for the dissipative Hamiltonian and analyze the uncertainties (Δr and Δp) and the quantum mechanical expectation value of energy (⟨E⟩) in terms of time (t), damping parameters and flux parameter (v). For the Caldirola-Kanai model, we observe that the flux parameter v decreases the energy dissipation in a quantum dot for a certain range of t.
DOI: 10.6084/m9.figshare.14326558
title: Dissipative Dynamics and Uncertainty Measures of a Charged Oscillator in the Presence of the Aharonov-Bohm Effect

description: We analyze the effects of dissipation in a charged oscillator in the presence of the Aharonov-Bohm effect by using time-dependent mass (m(t)) Hamiltonians. We consider two different models for the dissipative Hamiltonian and analyze the uncertainties (Δr and Δp) and the quantum mechanical expectation value of energy (⟨E⟩) in terms of time (t), damping parameters and flux parameter (v). For the Caldirola-Kanai model, we observe that the flux parameter v decreases the energy dissipation in a quantum dot for a certain range of t.
DOI: 10.6084/m9.figshare.14326559.v1
title: Experimental investigation of Stokes’ law on disks: a low-cost approach by video analysis of damped oscillations

description: In this work we present a low-cost activity that aims to investigate the drag force, which acts on the geometry of a disc, through the damped oscillations of a mass-spring system. Using cardboard disks of different radii and controlling the mass of the oscillatory system, keeping it fixed, we studied the influence of the exclusive variation of the magnitude of the drag force on the dynamics of this system, by varying the radius of the disk, keeping all the others fixed system accessible parameters. The video analysis technique is used to track the movement of the system, leading the student to investigate and draw conclusions about the functional dependence of the viscous frictional force with the radius of the disk, as well as to obtain the spring elastic constant and an estimate for the thickness of the disks.
DOI: 10.6084/m9.figshare.14326559
title: Experimental investigation of Stokes’ law on disks: a low-cost approach by video analysis of damped oscillations

description: In this work we present a low-cost activity that aims to investigate the drag force, which acts on the geometry of a disc, through the damped oscillations of a mass-spring system. Using cardboard disks of different radii and controlling the mass of the oscillatory system, keeping it fixed, we studied the influence of the exclusive variation of the magnitude of the drag force on the dynamics of this system, by varying the radius of the disk, keeping all the others fixed system accessible parameters. The video analysis technique is used to track the movement of the system, leading the student to investigate and draw conclusions about the functional dependence of the viscous frictional force with the radius of the disk, as well as to obtain the spring elastic constant and an estimate for the thickness of the disks.
DOI: 10.6084/m9.figshare.14326561
title: On the capacitance of a sphere in the presence of another nearby conducting sphere

description: We present the numerical analysis of the capacitance dependence of a conducting sphere on the distance to another sphere and its relative size. Among other results, we find that the greatest deviations from the model of a secluded sphere are observed for the case of the presence of infinite conducting plane near it. We provide a simple physical explanation of this fact. For example, our numerical calculations show that the value of relative error in the determination of the sphere capacitance is equal to 5% if the distance from the sphere center to the infinite plate is ten times more than its radius. The consideration of this problem will be useful for advanced undergraduates, who study the methods for solving electrostatic problems.
DOI: 10.6084/m9.figshare.14326561.v1
title: On the capacitance of a sphere in the presence of another nearby conducting sphere

description: We present the numerical analysis of the capacitance dependence of a conducting sphere on the distance to another sphere and its relative size. Among other results, we find that the greatest deviations from the model of a secluded sphere are observed for the case of the presence of infinite conducting plane near it. We provide a simple physical explanation of this fact. For example, our numerical calculations show that the value of relative error in the determination of the sphere capacitance is equal to 5% if the distance from the sphere center to the infinite plate is ten times more than its radius. The consideration of this problem will be useful for advanced undergraduates, who study the methods for solving electrostatic problems.
DOI: 10.6084/m9.figshare.14326562
title: The discontinuity of the electric field in a spherical charge distribution: a topological invariant

description: This article adds to the other recent ones that have been published, mainly in this magazine that is, in our view, becoming a forum for discussion of this which is the electric field on the surface of a charged spherical conductor. We recently published an article that discussed three models for finding the recalcitrant factor 1/2 that chase many fans of this electrostatic issue. In this way, this text was elaborated, exclusively, to try to clarify and oppose, some interpretations put in a later recent article [1] that defends a proper integral to find the stubborn factor. In this way, we reaffirm the method of superposition of the ring field to discuss the field’s behavior through a uniformly charged spherical surface, trying to reach a consensus.
DOI: 10.6084/m9.figshare.14326562.v1
title: The discontinuity of the electric field in a spherical charge distribution: a topological invariant

description: This article adds to the other recent ones that have been published, mainly in this magazine that is, in our view, becoming a forum for discussion of this which is the electric field on the surface of a charged spherical conductor. We recently published an article that discussed three models for finding the recalcitrant factor 1/2 that chase many fans of this electrostatic issue. In this way, this text was elaborated, exclusively, to try to clarify and oppose, some interpretations put in a later recent article [1] that defends a proper integral to find the stubborn factor. In this way, we reaffirm the method of superposition of the ring field to discuss the field’s behavior through a uniformly charged spherical surface, trying to reach a consensus.
DOI: 10.6084/m9.figshare.14326564
title: Foucault pendulum revisited, the determination of precession angular velocity using Cartesian coordinates

description: A review on the Foucault pendulum motion is presented using Cartesian coordinates for the ideal case and for small amplitude of oscillations. The choice of referential frames, the formulation and solution of Newton’s differential equation for the non-inertial frame of the Earth and the validity of the approximations used to simplify the determination of the solution are given. Using the angular position of the trajectory cusps, a new method to determine the precession angular velocity of the Foucault pendulum is shown. The pendulum bob trajectories and velocities for the referential frame in rotation with the Earth as well as for the inertial frame are given and the Chevilliet theorem was demonstrated. In addition, the pendulum bob trajectories are shown when an initial velocity is impinged in the direction perpendicular to the pendulum oscillation plane.
DOI: 10.6084/m9.figshare.14326564.v1
title: Foucault pendulum revisited, the determination of precession angular velocity using Cartesian coordinates

description: A review on the Foucault pendulum motion is presented using Cartesian coordinates for the ideal case and for small amplitude of oscillations. The choice of referential frames, the formulation and solution of Newton’s differential equation for the non-inertial frame of the Earth and the validity of the approximations used to simplify the determination of the solution are given. Using the angular position of the trajectory cusps, a new method to determine the precession angular velocity of the Foucault pendulum is shown. The pendulum bob trajectories and velocities for the referential frame in rotation with the Earth as well as for the inertial frame are given and the Chevilliet theorem was demonstrated. In addition, the pendulum bob trajectories are shown when an initial velocity is impinged in the direction perpendicular to the pendulum oscillation plane.
DOI: 10.6084/m9.figshare.14326565.v1
title: Free fall of two masses coupled by a spring in a uniform gravitational field

description: In solving classical mechanics problems many times we are guided by a feeling of familiarity and analogies. Nevertheless, not always this a good strategy. This is the case of the problem of two masses in free fall in a uniform field which we discuss in this paper.
DOI: 10.6084/m9.figshare.14326565
title: Free fall of two masses coupled by a spring in a uniform gravitational field

description: In solving classical mechanics problems many times we are guided by a feeling of familiarity and analogies. Nevertheless, not always this a good strategy. This is the case of the problem of two masses in free fall in a uniform field which we discuss in this paper.