- #1
George Keeling
Gold Member
- 183
- 42
- TL;DR
- confused by product symbol with two subscripts
I am looking at the Laughlin wave function and it contains the term
$$\prod_{j<k}^{N}\left(z_j-z_k\right)^q$$
In Wikipedia the lower index on ##\Pi## is ##1\le i<j\le N## and there is no upper index. I'm not sure what either mean. For example would
$$\prod_{j<k}^{N}\left(z_j-z_k\right)^q=\prod_{k=2}^{N}\left[\prod_{j=1}^{k-1}\left(z_j-z_k\right)^q\right]?$$
(It seems that ##k## cannot be 1 because there would be nothing to multiply in the second product). I'm not sure what else the expression could mean.
For ##N=3## that would give ##\ \left(z_1-z_2\right)^q\left(z_1-z_3\right)^q\left(z_2-z_3\right)^q## I think.
$$\prod_{j<k}^{N}\left(z_j-z_k\right)^q$$
In Wikipedia the lower index on ##\Pi## is ##1\le i<j\le N## and there is no upper index. I'm not sure what either mean. For example would
$$\prod_{j<k}^{N}\left(z_j-z_k\right)^q=\prod_{k=2}^{N}\left[\prod_{j=1}^{k-1}\left(z_j-z_k\right)^q\right]?$$
(It seems that ##k## cannot be 1 because there would be nothing to multiply in the second product). I'm not sure what else the expression could mean.
For ##N=3## that would give ##\ \left(z_1-z_2\right)^q\left(z_1-z_3\right)^q\left(z_2-z_3\right)^q## I think.