منابع مشابه
A Relativistic Quaternionic Wave Equation
We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved quantity which looks like helicity. The principle of superposition is retained in a slightly altered manner. External potentials can be introduced in a way th...
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Further results are reported for the one-component quaternionic wave equation recently introduced. A Lagrangian is found for the momentum-space version of the free equation; and another, nonlocal in time, is found for the complete equation. Further study of multiparticle systems has us looking into the mathematics of tensor products of Hilbert spaces. The principles of linearity and superpositi...
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Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from t...
متن کاملThe Relativistic Hermite Polynomials and the Wave Equation
Solutions of the homogeneous 2D scalar wave equation of a type reminiscent of the “splash pulse” waveform are investigated in some detail. In particular, it is shown that the “higher-order” solutions relative to a given “fundamental” one, from which they are obtained through a definite “generation scheme”, come to involve the relativistic Hermite polynomials. This parallels the results of a pre...
متن کامل- 1 - Electrically Pumped , Relativistic , Free Electron Wave Generators
Stimulated scattering induced by the longitudinal electric field of a pump wave is studied theoretically for the case of dense, relativistic electron beams traveling in cylindrical metal waveguides, Two processes are examined. In one, the pump wave decays parametrically into a slow and a fast space charge wave. In the other, it decays into a slow space charge wave and a TM wave of the guide. Th...
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ژورنال
عنوان ژورنال: Europhysics News
سال: 1977
ISSN: 0531-7479,1432-1092
DOI: 10.1051/epn/19770810001