00:01
In this question, look at the angular momentum operators, right? there are j plus minus j squared and also jz, right? and you asked to prove a few commentators.
00:14
Now, to prove those things, i will make use of the fundamental relations between the components of the operators, namely, jy, j -z equals i -j -x, and, well, i should put h bar here.
00:33
No, there's no hbar.
00:35
And just, no, there's a h bar here.
00:39
And then y, z and gd, gx equals ih, gy, and then gx, gy, and then gx, gy equals ih, gz.
00:53
Okay.
00:54
I will make use of this commentaries to prove things.
00:56
For example, you want to prove, you want to find the commentator between, g plus, well, g plus by definition, gx plus i, i, gy, i guess, right? probably divided by two, i forgot the definition, but roughly something like this.
01:18
And then you'll find this half, basically you'll find this to be two parts, g, z, g, x, plus i, g, g, z, y, y, y, y, y, y, y, y, and that would be, then you make use of the commentator between z and x, which is here, so you get h, j, y, y, y, y, j, y, y, y, and plus i, and j z and g, where, what's that? g z and j y, you get a minus i, jx, right? so you get a minus i h, jx...