Einstein's Diffusion and Probability-Wave Equations of Random ...
Einstein's Diffusion and Probability-Wave Equations of Random ...
Einstein's Diffusion and Probability-Wave Equations of Random ...
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Gauge Institute Journal,<br />
H. Vic Dannon<br />
xδ ( x) = 0<br />
6. If dx =<br />
1<br />
, ( x) = 1 1( x),2 1 1( x),3 1 1( x )...<br />
n<br />
[ − , ] [ − , ] [ − , ]<br />
δ χ χ χ<br />
2 2 4 4 6 6<br />
7. If dx =<br />
2<br />
,<br />
n<br />
8. If dx =<br />
1<br />
,<br />
n<br />
1 2 3<br />
δ ( x) = , , ,...<br />
2 2 2<br />
2 cosh x 2 cosh 2x 2 cosh 3x<br />
−x −2x −3x<br />
[0, ∞) [0, ∞) [0, ∞)<br />
δ( x) = e χ ,2 e χ , 3 e χ ,...<br />
x =∞<br />
∫<br />
9. δ( xdx ) = 1.<br />
x =−∞<br />
k =∞<br />
1 −ik( ξ−x<br />
)<br />
10. δξ ( − x)<br />
= e<br />
2π<br />
∫ dk<br />
k =−∞<br />
18
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