Klein–Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions

2010 ◽  
Vol 217 (6) ◽  
pp. 2710-2723 ◽  
Author(s):  
Joseph M. Lindquist ◽  
Francis X. Giraldo ◽  
Beny Neta
Keyword(s):  
Boundary Conditions ◽  
Gordon Equation ◽  
Unbounded Domains ◽  
High Order ◽  
Spectral Elements ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 200 ◽  
Author(s):  
He Yang
Keyword(s):  
Numerical Methods ◽  
Gordon Equation ◽  
Free Particle ◽  
High Order ◽  
Linear Momentum ◽  
Relativistic Quantum Mechanics ◽  
Optimal Error Estimates ◽  
Numerical Schemes ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Theoretical Investigation ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

Particles ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 325-332
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
The Given ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein–Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex ω-plane. In particular, it is proved that this solution does not contain any superluminal components under the given boundary conditions. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of the neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that it behaves as a localized wave for sufficiently small energies.

Sign in / Sign up

Export Citation Format

Share Document