Partition function calculation

[weiss_tal]

Hello all,

I have some trouble understanding the partition function. In wikipedia it is written that the partition function needs to be calculated with the multiplicity of the states:

z=SUM[g(E)exp(-BE)]

where g(E) is the multiplicity of the states corresponding to energy E.

It is also well known that the relative probability of two different states with different energy is P(E1)/P(E2) = exp(-BE1)/exp(-BE2).

According to the partition function which is the sum of all probabilities, the expression above should be g(E1)exp(-BE1)/g(E2)exp(-BE2)

What is true... ?
Thank you for helping.

 

[Bill_K]

The relative probability of the system being in *specific* states with energy E₁ and E₂ is P(E₁)/P(E₂) = exp(-βE₁)/exp(-βE₂). But the relative probability of the system being in *any* state with energy E₁ and E₂ is P(E₁)/P(E₂) = g(E₁)exp(-βE₁)/g(E₂)exp(-βE₂).

 

[weiss_tal]

Thanks mister K.
That was very helpful!

Tal.