# Interpreting microcanonical distribution

 P: 24 I'm trying to interpret the expression of a microcanonical distribution for energy $E_0$ of a particle of mass m moving about a fixed centre to which it is attracted by a Coulomb potential, $Zr^{-1}$, where $Z$ is negative. The function expression looks like this: $ρ_{E_0}(\textbf{r,p}) = \delta(E_0 - \frac{1}{2}m^{-1}p^2-Zr^{-1})$. Most of the stuff in the expression is understandable, but I am not sure what the delta signifies here. Any help? Thanks! J
 C. Spirit Sci Advisor Thanks P: 5,661 In the microcanonical ensemble the system lies on a surface of constant energy in phase space so the probability distribution has to vanish off of the constant energy surface. The argument in the delta function just represents this surface.
 P: 24 So $E_0 ≠ \frac{1}{2}m^{-1}p^2+Zr^{-1} → ρ_{E_0}(\textbf{r,p}) = 0$ ? Does the original expression actually say something about the distribution itself, or only about this property?
C. Spirit
 Quote by jjr So $E_0 ≠ \frac{1}{2}m^{-1}p^2+Zr^{-1} → ρ_{E_0}(\textbf{r,p}) = 0$ ?