That is formally how you normalize it. You can't normalize a probability distribution function unless you know the sum of all values. However, In practice we can occasionally cheat and just consider a handful of states (and thus just normalize over those).
@@MertErcan95 Now we're getting into definitions, but formally a partition sum doesn't necessarily need to sum over the same states used to normalize weights, or alternatively speaking - weights merely need to be relatively correct, they don't *have* to sum to unity, although that's of course a convenient choice - once we DO have the total sum so we could normalize them. In that case, the denominator would indeed be 1.
How was this one video more helpful than the entire lecture notes for my statistical mechanics course
Why divide with the partition function on the total energy formula? The probability/weight function of a state is already normalized
That is formally how you normalize it. You can't normalize a probability distribution function unless you know the sum of all values. However, In practice we can occasionally cheat and just consider a handful of states (and thus just normalize over those).
@@eriklindahl I think he is still right though? Why normalize twice, it is alreafy normalized in the definition of w as he pointed out.
@@MertErcan95 Now we're getting into definitions, but formally a partition sum doesn't necessarily need to sum over the same states used to normalize weights, or alternatively speaking - weights merely need to be relatively correct, they don't *have* to sum to unity, although that's of course a convenient choice - once we DO have the total sum so we could normalize them. In that case, the denominator would indeed be 1.
Thank you so much, this was very enlightening!
Thanks