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Interpreting microcanonical distribution 
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#1
Sep314, 10:32 AM

P: 24

I'm trying to interpret the expression of a microcanonical distribution for energy [itex]E_0[/itex] of a particle of mass m moving about a fixed centre to which it is attracted by a Coulomb potential, [itex]Zr^{1}[/itex], where [itex]Z[/itex] is negative. The function expression looks like this:
[itex]ρ_{E_0}(\textbf{r,p}) = \delta(E_0  \frac{1}{2}m^{1}p^2Zr^{1})[/itex]. Most of the stuff in the expression is understandable, but I am not sure what the delta signifies here. Any help? Thanks! J 


#2
Sep314, 10:35 AM

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.



#3
Sep314, 11:25 AM

P: 24

So [itex] E_0 ≠ \frac{1}{2}m^{1}p^2+Zr^{1} → ρ_{E_0}(\textbf{r,p}) = 0 [/itex] ?
Does the original expression actually say something about the distribution itself, or only about this property? 


#4
Sep314, 11:38 AM

C. Spirit
Sci Advisor
Thanks
P: 5,661

Interpreting microcanonical distribution



#5
Sep314, 12:59 PM

P: 24

Great! Thanks for helping me out



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