# From micro-canonical to canonical partition function

If total energy of a system (ideal gas) with energy $E$ and number of atoms $N$ and volume $V$ is given, how do I calculate what is the probability that an atom has energy $\epsilon$.

I tried to do it this way, probability would be given by the number of microstates associated to a system with energy $\Omega(E-\epsilon)$ divided by the total number of microstates $\int_0^E\Omega (E-\epsilon)d\epsilon$. I tried to convert this expression to the partition function form, but in case of partition functions (canonical ensemble), $\epsilon$ runs from $0$ to $\infty$, but here energy of system is fixed. So I'm stuck,

Please suggest something.

• Do you mean $\Omega(E = \epsilon)$ in your formulas? – The Vee Feb 20 '18 at 10:23
• No, since total energy is $E$ and system has energy $\epsilon$, so number of microstates is the number for remaining energy $E-\epsilon$. – Ankur Singh Feb 20 '18 at 10:28
• Assuming the states of the system are non-degenerate. – Ankur Singh Feb 20 '18 at 10:29