gordon equation उदाहरण वाक्य

In 1967 Gerald Feinberg hypothesized the existence of tachyons as particles represented by the imaginary solutions of relativistic quantum wave equations, such as the Klein-Gordon equation.
Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schr�dinger equation with a covariant equation such as the Klein Gordon equation or the Dirac equation.
The Schr�dinger equation can also be derived from a first order form similar to the manner in which the Klein-Gordon equation can be derived from the Dirac equation.
Common examples of linear PDEs include the heat equation, the wave equation, Laplace's equation, Helmholtz equation, Klein Gordon equation, and Poisson's equation.
For example, the Klein Gordon equation is the classical equation of motion for a free scalar field, but also the quantum equation for a scalar particle wave-function.

Continuing with the nonlinear Klein Gordon equation, using the average variational principle on equation, the wave action equation becomes by variation with respect to the wave phase \ theta:
Many exactly solvable models have soliton solutions, including the Korteweg de Vries equation, the nonlinear Schr�dinger equation, the coupled nonlinear Schr�dinger equation, and the sine-Gordon equation.
The Fourier transform ( in all four variables ) of such measures yields positive-energy, finite-energy solutions of the Klein-Gordon equation defined on Minkowski space, namely
The sine-Gordon equation is a relativistic wave equation in 1 + 1 dimensions that also exhibits the soliton phenomenon and which became an important model of solvable relativistic field theory.
Mathematically, a semifluxon can be constructed by joining two tails of conventional ( integer ) fluxon ( kink of the sine-Gordon equation ) at the 0-? boundary.