No abstract

We discuss the usefulness and physical interpretation of a simple and general way of constructing sequences of functions that converge to the Dirac delta function. The main result, which seems to have been largely overlooked, includes most of the δ-function converging sequences found in textbooks, is easily extended, and can be used to introduce many useful generalized functions to physics students with little mathematical background. We show that some interesting delta-function identities are simple consequences of the one discussed here. An illustrative example in electrodynamics is also analyzed, with the surprising result that the formalism allows as a limit an uncharged massless particle which creates no electromagnetic field, but has a nonzero electromagnetic energy–momentum tensor.

Quantization of generalized Lagrangian systems suggests that wave functions for elementary particles must be defined on the kinematical space rather than on configuration space. For spinning particles the center of mass and center of charge are different points. Their separation is of the order of the Compton wavelength. Spinl/2 particles arise if the classical model rotates but no half integer spins are obtained for systems with spin of orbital nature. Dirac's equation is obtained when quantizing the classical relativistic spinning particles whose center of charge is circling around its center of mass at the speed c. Internal orientation of the electron completely characterizes its Dirac's algebra. 3380

The subtleties in the derivation of the retarded Liénard–Wiechert potential for a point charge are stressed by explicitly computing and drawing the retarded shape of a moving sphere. This shape is the effective integration region for the charge density and it is computed, with the aid of the ‘‘information collecting sphere,’’ in the limit of vanishing radius (or, equivalently, from the point of view of a remote observer).

Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.We analyze the initial motion of an elastic bar that is suddenly released after being hung from one end. The analytical solutions uncover some unexpected properties, which can be checked with a digital camera or camcorder in an alternative setup in which a spring is substituted for the bar. The model and the experiments are useful for understanding the similarities and differences between the elastic properties of bars and springs. Students can use the simple experiments to improve their understanding of elastic waves.