00:01
The angular momentum has two contributions, one coming from the angular momentum itself, which is given by the summation, from ml equals to minus l, up to l of ml, h -bar.
00:16
And another contribution comes from the spin, which is given by the summation, from ms equals to minus 1 -half, up to plus 1 -half, of h -bar, of h -b, times ms.
00:34
Note that for complete subshells the summation of the spin contribution will always vanish because it will always be equals to one -half minus one -half times each bar this is equal to zero.
00:52
Then we are left with this contribution that comes from the angular momentum itself from the magnetic quantum numbers.
01:00
We can see the following.
01:02
So this can be written as the summation from m l equals to minus l up to zero of m l hbar plus the summation from m l equals to zero to l of m l hbar.
01:22
Then we can write this term here in another way...