- #1
tomyuey938
- 14
- 0
This is from self-study coursework rather than homework. I hope it's ok in this forum.
I'm following a statistical mechanics lecture on youtube, and the professor is deriving the average energy as a function of the partition function. He goes:
-1/Z dZ(beta)/d beta = -dlnZ(beta) / d beta
where Z(beta) is the partition function = e^{-(beta) E}.
I spent an hour trying to figure out why the LHS equals the RHS (from both directions, including using differentiation by substitution) but I just can't figure out how he does it.
Perhaps this is a really simple question (and if so, I apologies for my stupidity) but can anyone tell me how to go between the two steps?
Thank you in advance!
I'm following a statistical mechanics lecture on youtube, and the professor is deriving the average energy as a function of the partition function. He goes:
-1/Z dZ(beta)/d beta = -dlnZ(beta) / d beta
where Z(beta) is the partition function = e^{-(beta) E}.
I spent an hour trying to figure out why the LHS equals the RHS (from both directions, including using differentiation by substitution) but I just can't figure out how he does it.
Perhaps this is a really simple question (and if so, I apologies for my stupidity) but can anyone tell me how to go between the two steps?
Thank you in advance!