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relativistic sinusoidal wave function

Relativistic Sinusoidal Wave Function

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture" - Bertrand Russell ( 1872 - 1970 )

§ Definitions:


sinusoidal angular frequency


sinusoidal phase velocity


sinusoidal wave number


sinusoidal wavelength


sinusoidal phase cycle

§ Derivations:

(i). Therefore,

sinusoidal wave function derivations

(ii). Relativistic sinusoidal wave function:

An observer in stationary S system would therefore view a sinusoidal wave form as  

sinusoidal sine function

but another observer in relatively moving S' system would view the same sinusoidal wave form as follows: 

relativistic sinusoidal wave function

relativistic sinusoidal wave function

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relativistic sinusoidal wave function