- #1
alejandrito29
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In a aislate system, the probability on a microcanonical state \Gamma is
p(\Gamma ) = 1/K , if E<H<E + ΔE, and 0 on otherwise
with K = \int_{\Gamma : E<H<E+ΔE} d \Gamma
a) Show that ΔE →0, then
p(\Gamma) = \frac{\delta (E-H)}{\int_{\Gamma : H=E} \delta(E-H)}
b) Show that if use the change of variable \Gamma \to (X,a), with X are 6N-1 coordinates abaut the surface H=E, and a is a perpendicular coordinate to this surface at the point X, then
\int_D \delta (E-H) d \Gamma = \int_{D_E} \frac{ d X}{ || \frac{dH}{d \Gamma}||}
The rules of this forums says that i says my tried, but, sincerely i don't idea abaut this problem, i think on Taylor for the question a), but i don't have result.
p(\Gamma ) = 1/K , if E<H<E + ΔE, and 0 on otherwise
with K = \int_{\Gamma : E<H<E+ΔE} d \Gamma
a) Show that ΔE →0, then
p(\Gamma) = \frac{\delta (E-H)}{\int_{\Gamma : H=E} \delta(E-H)}
b) Show that if use the change of variable \Gamma \to (X,a), with X are 6N-1 coordinates abaut the surface H=E, and a is a perpendicular coordinate to this surface at the point X, then
\int_D \delta (E-H) d \Gamma = \int_{D_E} \frac{ d X}{ || \frac{dH}{d \Gamma}||}
The rules of this forums says that i says my tried, but, sincerely i don't idea abaut this problem, i think on Taylor for the question a), but i don't have result.
