Self-action of a point charge in classical electrodynamics

A direct calculation demonstrates that the causal Green function for classical equations of an electromagnetic field contains an additional singular term cancelling the divergence in the self-action of a point charge. Thus, the problem of mass renormalization is avoided. An exact relativistic expression for the self-action force is presented as a sum of two terms. The first one gives the radiation damping and the second one describes the electromagnetic component of the particle momentum depending on its velocity and acceleration. Accordingly, the work of the force also consists of two terms: the radiation energy and the electromagnetic component of the particle energy. To perform the calculations, we have to extend the radial spherical coordinate in the δ-function argument to negative values. © 1996 Plenum Publishing Corporation

Interaction of circling relativistic charges and interference in their radiation

The radiation emitted by two charges circling at opposite ends of a diameter at arbitrary uniform speed is considered, with special attention being paid to interference effects. The difference in the rate of radiation from the system and the sum of the powers emitted separately by each circling charge is shown to be equal to the work done by the particles on each other through their exact Liénard-Wiechert fields, in accordance with the Poynting theorem. Some peculiarities of the radiation at high and low speeds are noted and explained. © 1997 American Association of Physics Teachers

Self-action of a point charge in classical electrodynamics

A direct calculation demonstrates that the causal Green function for classical equations of an electromagnetic field contains an additional singular term cancelling the divergence in the self-action of a point charge. Thus, the problem of mass renormalization is avoided. An exact relativistic expression for the self-action force is presented as a sum of two terms. The first one gives the radiation damping and the second one describes the electromagnetic component of the particle momentum depending on its velocity and acceleration. Accordingly, the work of the force also consists of two terms: the radiation energy and the electromagnetic component of the particle energy. To perform the calculations, we have to extend the radial spherical coordinate in the δ-function argument to negative values. © 1996 Plenum Publishing Corporation

One-dimensional hydrogen atom: A singular potential in quantum mechanics

A generalized Laplace transform approach is developed to study the eigenvalue problem of the one-dimensional singular potential V = -e2/\x\. Matching of solutions at the origin that has been a matter of much controversy is, thereby, made redundant. A discrete and non-degenerate bound-state spectrum results. Existing arguments in the literature that advocate (a) a continuous spectrum, (b) a degeneracy of energy levels as a result of a hidden O(2) symmetry, (c) an infinite negative energy state and (d) an impenetrable barrier at the origin are found to be untenable. It is argued that a judicious use of generalized functions, coupled with some classical considerations, enables the conventional method of solving the problem to recover precisely the same results which are shown to be in accord with an accurate semiclassical analysis of the problem