A set of supersymmetric partners of the Rosen-Morse potential is generated. The corresponding physical properties are studied-in particular, the change in intensity of the singularities at the boundaries of the domain.
An analytical approximation of a pendulum trajectory is developed for large initial angles. Instead of using a perturbation method, a succession of just two polynomials is used in order to get simple integrals. By obtaining the approximated period, the result is compared with the Kidd–Frogg and Hite formulas for the period which are very close to the exact solution for the considered angle.
The motions of a spin-less point-like charged particle predicted by the Landau-Lifshitz equation and the Hammond method are obtained for a step electric field, a smooth step electric field and an electromagnetic pulse by using analytical and numerical solutions. In addition to Hammond method not presenting the so-called constant force paradox, using step force brings out the apparent physical contradictions of Landau-Lifshitz equation regarding energy conservation. Nevertheless, a smooth step force shows the consistency of the Landau-Lifshitz equation. Unlike other cases, the electromagnetic pulse shows another fundamental difference between the two models. Finally, an analysis of the Hammond method is made.
The classical central field is analyzed within the Hammond theory of radiation reaction force. For the attractive Coulomb field, the trajectories deduced from Ford and Hammond equations are numerically obtained. Ford and Hammond equations are rewritten by using a recent correction to the non-relativistic equations for charged point particles which include a radiation reaction force term. Also, for the attractive Coulomb case, the trajectories are numerically obtained for both corrected equations. A comparison between all these trajectories is made. It is proved that Hammond equation satisfies the constraint proposed by Dirac of getting an equation of motion which should make the electron in the hydrogen atom spiralling inwards and ultimately falling into the nucleus. A further analysis of the applicability of such a theory is described for experiments particularly in Plasma Physics and some comments are made for the generalization of Hammond equation to General Relativity.
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