00:01
Okay, so we have a ket that's given like this in terms of angular momentum eigenstates.
00:11
The corresponding brad looks like this, in terms of the corresponding eigenstates, and we want to look at the operator jx operating on these states.
00:25
So written in terms of the raising and lowering operators.
00:30
So if i use a raising and lowering operator and hit it on a typical state, the typical ket, it looks like that.
00:43
And if i hit the lowering operator on a typical state, it looks like that.
00:57
Okay.
01:01
Now, one thing i want to observe like from the very beginning is this really restricts setting my states like this.
01:11
It really restricts what i'm going to get when i apply these rising and lowering operator.
01:21
So my expectation value of jx.
01:25
So we write out the bra and the operator in terms of our raising and lowering operators and the ket.
01:39
Looks like that.
01:40
Okay.
01:42
Now let's expand that a little bit.
01:46
Now, for instance, one of the things that i notice, if i take the raising operator, and i hit it on the state j1, it's going to produce the state j2.
02:00
But i don't have a state j2 in the braf, so it's going to give me zero expectation value.
02:12
Same thing when i hit j minus on the state j0.
02:17
There's no state j minus 1 over here...