gordon equation वाक्य
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- For the Klein Gordon equation, the general form of the Schr�dinger equation is inconvenient to use, and in practice the Hamiltonian is not expressed in an analogous way to the Dirac Hamiltonian.
- The Dirac equation is a relativistic quantum mechanical wave equation invented by Paul Dirac in 1928 ( Dirac 1928a, 1928b ) originally designed to overcome the criticism of the Klein-Gordon Equation.
- This embedding is connected with the fact that one can get the Schr�dinger equation from the massless Klein Gordon equation through parabolic sub-algebra of SO ( 2, d + 2 ).
- This is the original form of the sine-Gordon equation, as it was considered in the nineteenth century in the course of investigation of asymptotic lines parameterized with respect to the arc length.
- In this form, the fraction 4 \ pi / ( k ^ 2 + m ^ 2 ) is seen to be the propagator or Green's function of the Klein Gordon equation.
- The first basis for relativistic quantum mechanics, i . e . special relativity applied with quantum mechanics together, was found by all those who discovered what is frequently called the Klein Gordon equation:
- Afterwards, a representation of the form ( ) was found for many other physically interesting nonlinear equations, like the Kadomtsev Petviashvili equation, sine-Gordon equation, nonlinear Schr�dinger equation and others.
- The higher-spin algebra constructed above can be shown to be the symmetry algebra of the three-dimensional Klein-Gordon equation \ square _ 3 \ phi ( x ) = 0.
- The nonlinearity of this model leads either to the exactly integrable sine-Gordon equation which admits topological and dynamical solitons, or to the important equation of stochastic theory, the Taylor Chirikov map.
- These are essentially the solutions of the Dirac equation which describes the behavior of the electron's probability amplitude and the Klein Gordon equation which describes the behavior of the photon's probability amplitude.
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