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 />
<strong>and</strong> writes his integral as<br />
Δ=∞ Δ=∞ 2<br />
Δ=∞<br />
f<br />
1 f<br />
2<br />
fxt (,) δ ∂<br />
( ) d ( ) d ( ) d ..<br />
x<br />
δ ∂<br />
∫ Δ Δ + Δ Δ Δ + Δ<br />
2!<br />
δ Δ Δ +<br />
∂<br />
∫ ∫<br />
2<br />
∂x<br />
Δ=−∞ Δ=−∞ Δ=−∞<br />
He observes that the odd integrals vanish<br />
Δ=∞<br />
∫ Δδ( Δ) dΔ = 0,<br />
Δ=−∞<br />
Δ=∞<br />
∫<br />
Δ=−∞<br />
Δ 3 δ( Δ) dΔ = 0<br />
………………………<br />
He only misses that the even integrals vanish as well.<br />
Indeed, the sifting by<br />
δ( Δ)<br />
, gives<br />
k<br />
Δ = 0 .<br />
Δ= 0<br />
In particular, his Drift Coefficient, which is [p.131]<br />
D<br />
Δ=∞<br />
∫<br />
2ϕ( ) dΔ,<br />
Δ=−∞<br />
1<br />
= Δ Δ<br />
2τ<br />
vanishes,<br />
<strong>and</strong> his <strong>Diffusion</strong> Equation [equation 18, p. 132]<br />
collapses to<br />
2<br />
∂f<br />
∂ f<br />
= D<br />
∂t<br />
2<br />
∂x<br />
∂ f =<br />
∂t<br />
0 .<br />
,<br />
6
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