Qm notation

[g.lemaitre]

deleted

 

[Muphrid]

Do you know what the brackets mean in general?

Edit: pay attention to this line in particular.

Beware: The average of the squares, $\langle j^2 \rangle$, is not equal, in general, to the square of the average, $\langle j \rangle ^2$

This tells you very explicitly what the interpretation of both quantities should be.

 

[g.lemaitre]

I didn't see that sentence the square of the average is not the same as the average of squares. But now i do.

 

[g.lemaitre]

Nevertheless I'm truly amazed that you saw the question almost the moment I posted it and answered it in about 5 seconds. Wow!

 

[jedishrfu]

I think the <> notation just means average.

so the <j^2> means the average of the squares of j values

and <j>^2 is the square of the average of j values

 

[g.lemaitre]

But I guess what the brackets mean is that you have the take the average of what is between them, so pretend { is a bracket. If you know the latex for brackets please let me know.

{j^2} where j is 2,3,4 would be the average of 4 9 16 hence a little above 9 whereas {j}^2 would be 9 exactly, right?

 

[Muphrid]

Use \langle and \rangle for pretty brackets (not horrendously bad ones, which are what <> give you).

Otherwise, yes, you have the basic idea now. You should be accustomed to seeing $\langle j^2 \rangle - \langle j \rangle^2 = \sigma_j^2$ as well. This is one formula for the variance.