scholarly journals One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum

1984 ◽  
Vol 94 (4) ◽  
pp. 523-535 ◽  
Author(s):  
Ingrid Daubechies
Keyword(s):  
Kinetic Energy ◽  
Discrete Spectrum ◽  
Relativistic Kinetic Energy

A nonperturbative treatment of radiative decays and the relativistic kinetic energy in heavy quarkonia

1984 ◽  
Vol 23 (3) ◽  
pp. 275-280 ◽  
Author(s):  
P. Falkensteiner ◽  
D. Flamm ◽  
F. Sch�berl
Keyword(s):  
Kinetic Energy ◽  
Heavy Quarkonia ◽  
Radiative Decays ◽  
Relativistic Kinetic Energy

scholarly journals Relativistic mass due to a dilatant vacuum leads to a quantum reformulation of the relativistic kinetic energy

2020 ◽  
Vol 98 (2) ◽  
pp. 142-147
Author(s):  
Marco Fedi
Keyword(s):  
Kinetic Energy ◽  
Higgs Field ◽  
Lorentz Factor ◽  
Viscous Force ◽  
Dark Sector ◽  
Potential Term ◽  
Relativistic Mass ◽  
Planetary Orbits ◽  
Quantum Mechanism ◽  
Relativistic Kinetic Energy

Relativistic mass change with speed is considered here as the effect of a viscous, dilatant vacuum, whose apparent viscosity is related to the Lorentz factor. Transient solid-like vacuum due to shear stress is presented as the reason why vacuum prevents the speed of massive objects from being indefinitely increased. Such a vacuum – that in a previous study allowed to exactly calculate the Pioneer anomaly, Mercury’s perihelion precession, and was shown to be compatible with stable planetary orbits – leads here to a quantum formula for the relativistic kinetic energy. A formula which distinguishes between the case of accelerated charges in a vacuum, for which a Stokes–Einstein radius comes into play, and the case of accelerated macroscopic bodies, for which the quantum potential term vanishes. In this way, incidentally, one obtains again correct results for the Pioneer 10, confirming the role of vacuum’s viscous force. This description of a quantum mechanism underlying the relativistic kinetic energy may be also helpful in constructing a theory of quantum relativity and may even tell us more about the interactions of matter with the Higgs field and the dark sector: two issues which can be themselves linked to a dilatant vacuum.

scholarly journals Localization Error Estimate for the Massless Relativistic Kinetic Energy Operator

2016 ◽  
Vol 11 (2) ◽  
pp. 36-43
Author(s):  
J-M. Barbaroux ◽  
V. Vougalter ◽  
S. Vugalter
Keyword(s):  
Kinetic Energy ◽  
Error Estimate ◽  
Energy Operator ◽  
Localization Error ◽  
Kinetic Energy Operator ◽  
Relativistic Kinetic Energy

Including the relativistic kinetic energy in a spline-augmented plane-wave band calculation

1997 ◽  
Vol 55 (11) ◽  
pp. 6666-6669 ◽  
Author(s):  
G. M. Fehrenbach ◽  
G. Schmidt
Keyword(s):  
Kinetic Energy ◽  
Plane Wave ◽  
Wave Band ◽  
Augmented Plane Wave ◽  
Band Calculation ◽  
Relativistic Kinetic Energy

RELATIVISTIC CORRECTIONS OF THE α2-ORDER FOR THE TOTAL ENERGY AND THE MINIMUM PRESSURE IN THE THOMAS–FERMI THEORY

2002 ◽  
Vol 16 (23n24) ◽  
pp. 901-906 ◽  
Author(s):  
V. F. TARASOV
Keyword(s):  
Kinetic Energy ◽  
Total Energy ◽  
Electron Gas ◽  
Degenerate Electron ◽  
Fermi Theory ◽  
Minimum Pressure ◽  
Thomas Fermi ◽  
Relativistic Corrections ◽  
Relativistic Kinetic Energy ◽  
Degenerate Electron Gas

The total relativistic kinetic energy of the Thomas–Fermi atom is Ekr = Ek + Er, where Ek = κk ∫ ρ5/3dv and Er = -κr ∫ ρ7/3dv + o(α2), [Formula: see text]. The minimum pressure of a relativistic degenerate electron gas is [Formula: see text]. In just the same way, the cases x = pμ / mc = 1 and x > 1 are explicitly considered.

scholarly journals The energy spectrum in a barotropic atmosphere

2008 ◽  
Vol 15 ◽  
pp. 17-22 ◽  
Author(s):  
M. V. Kurgansky
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Discrete Spectrum ◽  
Energy Spectra ◽  
Two Dimensional ◽  
Barotropic Model ◽  
Atmospheric Sciences ◽  
Rotating Sphere ◽  
Barotropic Atmosphere ◽  
Mathematical Techniques

Abstract. In a forced-dissipative barotropic model of the atmosphere on a spherical planet, by following mathematical techniques in (Thompson, P. D.: The equilibrium energy spectrum of randomly forced two-dimensional turbulence, Journal of the Atmospheric Sciences, 30, 1593–1598, 1973) but applying them in a novel context of the discrete spectrum on a rotating sphere, the "minus 2" energy spectrum for wavenumbers much greater than a characteristic wavenumber of the baroclinic forcing has been obtained if the forcing is taken in the simplest and most fundamental form. Some observation-based atmospheric kinetic energy spectra, with their slopes lying between "minus 2" and "minus 3" laws, are discussed from the perspective of the deduced "minus 2" energy spectrum.

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