309 research outputs found
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
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