However, the Schr�dinger equation does not apply to massless particles; instead the Klein-Gordon equation is required.
12.
A state or quantum field in such a representation would satisfy no field equation except the Klein-Gordon equation.
13.
For \ sigma = 0 the system is linear and the classical one-dimensional Klein Gordon equation is obtained.
14.
The Proca equation is closely related to the Klein Gordon equation, because it is second order in space and time.
15.
This criticism leveled against the Klein-Gordon equation, motivated Dirac to successfully seek an equation devoid of negative probabilities.
16.
Kruskal himself pioneered some of the generalizations, such as the existence of infinitely many conserved quantities for the sine-Gordon equation.
17.
Most of his work was on the deformation of surfaces, and in particular, he introduced the sine Gordon equation in 1862.
18.
The Klein Gordon equation was first considered as a quantum wave equation by Schr�dinger in his search for an equation describing de Broglie waves.
19.
Then the Codazzi-Mainardi equation expressing a compatibility condition between the first and second fundamental forms results in the sine-Gordon equation.
20.
The second member is indeed independent of time as can be shown by deriving and remembering that both and satisfy the Klein Gordon equation.
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