The Lorentz-Dirac equation (LDE) x 000 ? x 00 = d dx V (x) models the point limit of the Maxwell-Lorentz equation describing the interaction of a charged extended particle with the electromagnetic eld. Since (LDE) admits solutions which accelerate even if they are outside the zone of interaction, Dirac proposed to study so-called "non runaway" solutions satisfying the condition x 00 (t) ! 0 as ...

In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle. Typeset using REVTEX 1 Recently, Moshinsky and Szczepaniak [1] have proposed a new type of interaction in the Dirac equation which, besides the momentum, is also linea...

We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar’s separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate ...

We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac equation, exist. A partial set of translations between complex and complexified quaternionic quantum mechanics may be defined. a) e-mail address: [email protected]

We consider the Dirac equation with two different four-potentials of the plane electromagnetic waves. We derive the partial differential equation for the wave function, which is generalized form of the Volkov equation. We find the solutions of the Dirac equation for two orthogonal plane waves. We determine the modified Compton formula for the scattering of two photons on an electron.

We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton–Jacobi equation as the Dirac–Hamilton–Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the th...