Shape Invariant Potential and Semi-Unitary Transformations (SUT) for Supersymmetric Harmonic Oscillator in T4-Space

Constructing the Semi - Unitary Transformation (SUT) to obtain the supersymmetric partner Hamiltonians for a one dimensional harmonic oscillator, it has been shown that under this transformation the supersymmetric partner loses its ground state in T^{4}- space while its eigen functions constitute a complete orthonormal basis in a subspace of full Hilbert space. Keywords: Supersymmetry, Superluminal Transformations, Semi Unitary Transformations. PACS No: 14.80L

Radiation Induced Fermion Resonance

The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation induced fermion resonance.Comment: latex, 4 pages, no figure

Superluminal X-shaped beams propagating without distortion along a coaxial guide

In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039], we showed that localized Superluminal solutions to the Maxwell equations exist, which propagate down (non-evanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous non-dispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, geophysics, etc.). [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Coaxial cables; Bidirectional decomposition; Bessel beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (22 pages), plus 15 figures; in press in Phys. Rev.

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies

By a generalized bidirectional decomposition method, we obtain many new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; various of them being endowed with finite total energy. We construct, among the others, an infinite family of generalizations of the so-called "X-shaped" waves. [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Bidirectional decomposition; Bessel beams; X-shaped waves; Microwaves; Optics; Special relativity; Acoustics; Seismology; Mechanical waves; Elastic waves; Gravitational waves; Elementary particle physics].Comment: plain LaTeX file (29 pages), plus 11 figures. Replaced with addition of the FIGURES that were lacking (or poor) in the previous submissions. In press in Europ. Phys. Journal-

Chirped optical X-shaped pulses in material media

In this paper we analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shape after some propagation distance, while the ordinary chirped gaussian-pulses can recover their longitudinal shape only (since gaussian pulses suffer a progressive spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during the pulse propagation.Comment: Replaced with a much larger and deepened version (the number of pages going on from 4 to 24; plus 4 Figures added

Spin effects on the cyclotron frequency for a Dirac electron

The Barut--Zanghi (BZ) theory can be regarded as the most satisfactory picture of a classical spinning electron and constitutes a natural "classical limit" of the Dirac equation. The BZ model has been analytically studied in some previous papers of ours in the case of free particles. By contrast, in this letter we consider the case of external fields, and a previously found equation of the motion is generalized for a non-free spin-1/2 particle. In the important case of a spinning charge in a uniform magnetic field, we find that its angular velocity (along its circular orbit around the magnetic field direction) is slightly different from the classical "cyclotron frequency" eH/m which is expected to hold for spinless charges. As a matter of fact, the angular velocity results to depend on the spin orientation. As a consequence, the electrons with magnetic moment mu parallel to the magnetic field do rotate with a frequency greater than that of electrons endowed with mu antiparallel to H