Hitherto, we have focussed on applications of quantum mechanics to free particles or particles confined by scalar potentials. In the following, we will address the influence of a magnetic field on a charged particle. Classically, the force on a charged particle in an electric and magnetic field is specified by the Lorentz force law: Hendrik Antoon Lorentz 18531928 A Dutch physicist who shared t...

We find the Noether point symmetries for non–relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi–invariance transformation, a time–dependent rotation and a time–dependent spatial translation. The associated electromagnetic field satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding three classes ...

We consider the problem of nding rigorous results for the dynamics of a classical charged point particle interacting with the electromagnetic eld, as described by the standard Maxwell{Lorentz equations. Some results are given for the corresponding linearized system, i.e. the so called dipole approximation, in the presence of a mechanical linear restoring force. We regularize the system by takin...

We find the Lie point symmetries for non–relativistic two-dimensional charged particle motion. These symmetries comprise a quasi–inva-riance transformation, a time–dependent rotation, a time–dependent spatial translation and a dilatation. The associated electromagnetic fields satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding four clas...

As it is known a model of a charged particle with finite size is a good tool to consider the effects of self-action and backreaction, caused by electromagnetic radiation. In this work the " size " of a charged particle is induced by its stochastic Brownian vibration. Appropriate equation of particle's motion with radiation force is derived. It is shown that the solutions of this equation correc...

We discuss the equations of motion of test particles for a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric tensor of the fivedimensional manifold is allowed to depend on the fifth coordinate. This is the usual working scenario in brane-world, induced-matter theory and other Kaluza-Klein theories with large extra dimensions. We present a new version for the...

Trajectories of charged particle in combined poloidal, toroidal magnetic eld and rotation-induced unipolar electric eld superposed in Schwarzschild background geometry have been investigated extensively in the context of accreting black holes. The main purpose of the paper is to obtain a reasonably well insight on the e ect of spacetime curvature to the electromagnetic eld surrounding black hol...

The equation of motion for a charged particle moving in the ndimensional constant magnetic filed is obtained for any linear gauge and any metric tensor by generalization of Johnson and Lipmann’s approach. It allows to consider the magnetic orbits in the n-dimensional space. It is shown that the movement of a particle can always be decomposed into a number of two-dimensional cyclotronic motions ...

We review the formulation of the problem of electromagnetic self-interaction of a relativistic charged particle in the framework of the manifestly covariant classical mechanics of Stueckeleberg, Horwitz, and Piron. The gauge fields of this theory, in general, cause the mass of the particle to change. We study the four dynamical off-mass-shell orbit equations which result from the expansion of G...

We address the old question of whether or not a uniformly accelerated charged particle radiates, and consequently, if weak equivalence principle is violated by electrodynamics. We show that radiation has different meanings; some absolute, some relative. Detecting photons or electromagnetic waves is not absolute, it depends both on the electromagnetic field and on the state of motion of the ante...