The number of states for N identical particles with energy between E and E+dE

  • Thread starter pallab
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  • #1
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Homework Statement:

no of states for N identical free particles with energy between E and E+δE is proportional to -

Relevant Equations:

for microcanonical ensemble
the answer is NE^0.5 but my answer is E^0.5N
the # of state is Ω=( one particle phase-space volume)^N
one particle phase-space volume=integration of dq*integration of dp
from space part dq I get V and dp is converted into Energy E variable via E=p^2/2m
 

Answers and Replies

  • #2
192
82
considering 3D and the volume of sphere in 3N dimensional space
[tex]\sum_{i=1}^n (p_{ix}^2+p_{iy}^2+p_{iz}^2)=2mE[/tex]
I got volume of the shell is proportional to
[tex]E^{\frac{3N}{2}-1}dE[/tex]
 

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