# Statistical mechanics

1. Aug 27, 2013

### alejandrito29

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, sincerly i dont idea abaut this problem, i think on Taylor for the question a), but i dont have result.