Doppler Shifted “In” and “Out” Longitudinal Matter Waves as the Carriers of Particle Relativistic Momentum and Energy

Momentum and Kinetic Energy equations are developed from the hypothesis that oppositely directed components of harmonically oscillating pseudo standing waves pass through a quantum particle center and can be represented by Longitudinal Matter Waves that carry the particle’s momentum and energy. The Doppler effect on the component wave lengths allows the net forward momentum and kinetic energy to increase with speed well beyond classical values. De Broglie (1925) issues with stationary wavelength and moving pulse rate are resolved in a different manner. Because a quantum particle is considered to be nothing more than the sum of “in” and “out” matter waves focused through its center, whatever happens to these matter waves determines the future location of that center. This opens the door to physical explanations for gravity, interference, and the slowdown of light in transparent mediums. Gravity, for example, is shown in section 6, to possibly be caused by the local gradient in matter wave speed near a large body like earth.

Optimum point of acceleration of an electron inside the collisional plasma-filled elliptical waveguide

In this paper, the effect of the electron collision frequency with background ions on TMmr mode field components, the trajectory and the electron energy gain is studied. The field components of the TMmr mode in the elliptical waveguides are calculated. The ohmic heating for three different value of collision frequency calculated and the power losses is obtained. The deflection angle and acceleration gradient of an electron in the fields associated with a transverse magnetic (TM) wave propagating inside a elliptical waveguide for TMmr mode is studied. The relativistic momentum and energy equations for an electron are solved, which was injected initially along the propagation direction of the microwave. The results for TMmr mode are graphically represented. Finally, the optimum point of acceleration for the even mode TM11 is obtained and it is shown that in a cross section of elliptical waveguide optimum point is center of ellipse.

A VARIATIONAL FOCK-SPACE TREATMENT OF QUARKONIUM

The variational method and the Hamiltonian formalism of QCD are used to derive relativistic, momentum space integral equations for a quark–antiquark system with an arbitrary number of gluons present. As a first step, the resulting infinite chain of coupled equations is solved in the nonrelativistic limit by an approximate decoupling method. Comparison with experiment allows us to fix the quark mass and coupling constant, allowing for the calculation of the spectra of massive systems such as charmonium and bottomonium. Studying the results with and without the non-Abelian terms, we find that the presence of the non-Abelian factors yields better agreement with the experimental spectra.