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:

(i).

(ii).

(iii).

(iv).

(v).

§ Derivations:

(i). Therefore,

(ii). Relativistic sinusoidal wave function:

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

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

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